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Tuning graphene’s electronic and transport properties via adatom deposition Khademi, Ali 2017

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Tuning Graphene’s Electronic and Transport Propertiesvia Adatom DepositionbyAli KhademiM.Sc., Sharif University of Technology, 2009B.Sc., Sharif University of Technology, 2007A THESIS SUBMITTED IN PARTIAL FULFILLMENTOF THE REQUIREMENTS FOR THE DEGREE OFDoctor of PhilosophyinTHE FACULTY OF GRADUATE AND POSTDOCTORALSTUDIES(Physics)The University of British Columbia(Vancouver)August 2017c© Ali Khademi, 2017AbstractThis thesis investigates the effect of adatom deposition, especially alkali and heavyadatoms, on graphene’s electronic and transport properties. While there are manytheoretical predictions for tuning graphene’s properties via adatom deposition, onlya few of them have been observed. Solving this enigma of inconsistency betweentheory and experiment raises the need for deeper experimental investigation of thismatter. To achieve this goal, an experimental set up was built which enables us toevaporate different metal adatoms on graphene samples while they are at cryogenictemperatures and ultra-high vacuum (UHV) conditions.The critical role of in situ high-temperature annealing in creating reliable inter-actions between adatoms and graphene is observed. This contradicts the commonlyaccepted assumption in the transport community that placing a graphene sample inUHV and performing in situ 400-500 K annealing is enough to provide a reliableadatom-graphene interaction. Even charge doping by alkali atoms (Li), which isarguably the simplest of all adatom effects, cannot be achieved completely with-out in situ 900 K annealing. This observation may explain the difficulty manygroups have faced in inducing superconductivity, spin-orbit interaction, or similarelectronic modifications to graphene by adatom deposition, and it points toward astraightforward, if experimentally challenging, solution.The first experimental evidence of short-range scattering due to alkali adatomsin graphene is presented in this thesis, a result that contradicts the naive expecta-tion that alkali adatoms on graphene only cause long-range Coulomb scattering.The induced short-range scattering by Li caused decline of intervalley time andlength (i.e., enhancement of intervalley scattering). No signatures of theoreticallypredicted superconductivity of Li doped graphene were observed down to 3 K.iiCryogenic deposition of copper increased the dephasing rate of graphene. Thisincrease in dephasing rate is either a sign of inducing spin-orbit interaction or mag-netic moments by copper. No similar effect was observed for indium.iiiLay SummaryGraphene is the first known two-dimensional (2D) material with single atom thick-ness. Graphene’s 2D structure produces several interesting effects, including anextreme sensitivity to surface impurities. A positive aspect of this sensitivity to thesurface is that graphene’s electronic properties can be potentially changed in a dra-matic way by depositing individual metal atoms on a graphene sheet. For example,some light metals atoms (like Lithium) are expected to induce superconductivity, astate of zero electrical resistance, in this material. Alternatively, heavy metals (likeIndium) atoms are predicted to turn graphene into a new form of matter known asa topological insulator. However, these predictions have not been realized experi-mentally. This thesis tries to solve the surprising inconsistency between theoreticalpredictions and experiments in this remarkable material.ivPrefaceChapter 5 of this thesis is based on the following publication:[1] Khademi, A., Sajadi, E., Dosanjh, P., Bonn, D. A., Folk, J. A., Sto¨hr,A., Starke, U., Forti, S., “Alkali doping of graphene: The crucial role of high-temperature annealing”, Phys. Rev. B 94, 201405(R) (2016).This paper was authored by me, my supervisor, Dr. Joshua Folk, another PhDstudent in our group, Ebrahim Sajadi, our collaborators at the University of BritishColumbia, Pinder Dosanjh, and Dr. Douglas Bonn, and our collaborators at MaxPlanck Institute for Solid State Research, Alexander Sto¨hr, Dr. Ulrich Starke, andDr. Stiven Forti.Chapter 6 of this thesis is soon to be submitted for publication.The experimental setup was designed and built by the author under the super-vision of his supervisor, Dr. Joshua Folk and with the help of research engineer,Pinder Dosanjh, and with additional help from a former postdoc in the group, Dr.Julien Renard as well as Dr. Bart Ludbrook who was a PhD student of Dr. AndreaDamascelli at the time. The liquid helium cryostat, UHV chamber, and its partswere purchased or borrowed from Dr. Douglas Bonn’s group. My friend AmirHossein Masnadi, who is a PhD student at UBC electrical engineering, assistedme in building RC filters and measuring their response. Our collaborators at MaxPlanck Institute for Solid State Research provided us some SiC samples, whileother SiC samples were purchased. Ebrahim Sajadi transfered one CVD graphenesample onto a SiO2 substrate. Exfoliation of three exfoliated graphene samples wasdone by Rui Yang, a PhD student in our group, and Anuar Yeraliyev. However, allof the other fabrication processes like electron beam lithography were done by theauthor. The exfoliated graphene on boron nitride sample was totally made by avformer postdoc in our group, Dr. Matthias Studer. Numerous discussions withDr. Marcel Franz, Dr. Mark Lunderburg, Dr. Julien Renard, Dr. Silvia Folk, Dr.Douglass Bonn, Dr. Andrea Damascelli, Dr. Sarah Burke, Dr. Bart Ludbrook, Dr.Giorgio Levy, Pascal Nigge, and Andrew Macdonald improved the analyses andmeasurements of this project.viTable of ContentsAbstract . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . iiLay Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ivPreface . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . vTable of Contents . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . viiList of Tables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xiList of Figures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xiiAcknowledgments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xvii1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12 Experimental and Theoretical Background: Adatoms on Graphene 52.1 Graphene Hamiltonian and Dispersion Relation . . . . . . . . . . 62.2 Weak Localization in Graphene . . . . . . . . . . . . . . . . . . . 82.3 Adatoms’ Doping of Graphene . . . . . . . . . . . . . . . . . . . 102.4 Long-range and Short-range Scattering in Graphene due to Adatoms 112.4.1 Long-range Scattering due to Adatoms . . . . . . . . . . 122.4.2 Short-range Scattering due to Adatoms . . . . . . . . . . 132.5 Intervalley Scattering in Graphene . . . . . . . . . . . . . . . . . 162.6 Enhancement of Electron-Phonon Coupling and Induced Super-conductivity in Graphene by Alkali Adatoms . . . . . . . . . . . 18vii2.7 Enhancement of Spin-orbit Interaction by Heavy Adatoms in Graphene 193 UHV Cryogenic Evaporation and Measurement Chamber . . . . . . 233.1 Overview of Experimental Setup . . . . . . . . . . . . . . . . . . 233.2 Liquid Helium Flow Cryostat . . . . . . . . . . . . . . . . . . . . 253.3 Superconducting Magnet . . . . . . . . . . . . . . . . . . . . . . 253.4 Magnet Leads . . . . . . . . . . . . . . . . . . . . . . . . . . . . 273.5 Sample Holder and Bottom Connector . . . . . . . . . . . . . . . 303.6 Heater Stage . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 313.7 Electrical connections to the samples . . . . . . . . . . . . . . . . 333.8 Thermometers . . . . . . . . . . . . . . . . . . . . . . . . . . . . 353.9 30 K Shield . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 363.10 Thermal Evaporator: Lithium, Indium and Copper . . . . . . . . . 363.11 Wiring . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 393.12 Assembling Permanent Parts and Placing Removable Parts . . . . 413.13 Operation of Experimental Setup . . . . . . . . . . . . . . . . . . 444 Experimental Details . . . . . . . . . . . . . . . . . . . . . . . . . . 474.1 Graphene Samples . . . . . . . . . . . . . . . . . . . . . . . . . 484.1.1 Exfoliated Samples . . . . . . . . . . . . . . . . . . . . . 484.1.2 CVD Samples . . . . . . . . . . . . . . . . . . . . . . . 504.1.3 SiC Samples . . . . . . . . . . . . . . . . . . . . . . . . 514.1.4 Annealed and Unannealed Samples . . . . . . . . . . . . 524.2 Basics of Transport Measurements . . . . . . . . . . . . . . . . . 525 Alkali Doping of Graphene: The Crucial Role of High-temperatureAnnealing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 565.1 Alkali Doping of Graphene without High-temperature Annealing . 575.2 Alkali Doping of Graphene after Performing High-temperature An-nealing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 606 Alkali Induced Short-range Scattering: Intervalley Scattering in Li-doped Graphene . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 646.1 Weak Localization in Li-doped Graphene . . . . . . . . . . . . . 65viii6.2 Effect of Li Deposition on Intervalley Scattering in Graphene . . . 676.3 Effect of Li Deposition on Mobility and Diffusion Constant inGraphene . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 716.4 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 747 Li Induced Superconductivity? . . . . . . . . . . . . . . . . . . . . . 757.1 No Signatures of Superconductivity above 3 K . . . . . . . . . . . 757.2 Electronic Temperature . . . . . . . . . . . . . . . . . . . . . . . 777.3 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 808 Two Heavy Metal Candidates for Enhancing Spin-orbit Interactionin Graphene: Indium and Copper . . . . . . . . . . . . . . . . . . . 828.1 Indium-doped Graphene . . . . . . . . . . . . . . . . . . . . . . 838.2 Copper-doped Graphene . . . . . . . . . . . . . . . . . . . . . . 878.2.1 Trying to Evaporate Iridium Which Turned out to be Copper 878.2.2 Deposition of Copper . . . . . . . . . . . . . . . . . . . . 898.3 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 949 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 95Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 97A Detailed Design of Experimental Setup . . . . . . . . . . . . . . . . 116A.1 Magnet Frame . . . . . . . . . . . . . . . . . . . . . . . . . . . . 116A.2 Winding Superconducting Wire for Magnet . . . . . . . . . . . . 116A.3 Sample Holder and Bottom Connector . . . . . . . . . . . . . . . 121A.4 Gluing Male and Female Pins to Sample Holder and Bottom Con-nector . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 123A.5 30 K Outer Shield . . . . . . . . . . . . . . . . . . . . . . . . . . 130A.6 Electrical Feedthroughs and Wiring . . . . . . . . . . . . . . . . 131A.7 Filtering Johnson Noise in Wiring . . . . . . . . . . . . . . . . . 136A.8 RC Filters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 139A.9 Assembling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 142A.10 Measuring Magnet’s Field to Current ratio . . . . . . . . . . . . . 142ixA.11 Placing Removable Parts: Sample Holder, Cover Plate, Outer Shield,and Shutter . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 149A.12 Thermometery . . . . . . . . . . . . . . . . . . . . . . . . . . . . 150A.13 Other Parts of UHV Chamber . . . . . . . . . . . . . . . . . . . . 156A.14 Resistance Measurements . . . . . . . . . . . . . . . . . . . . . . 156B Mobility and Diffusion Constant of Unannealed Samples . . . . . . 158xList of TablesTable 2.1 The conductivity and mobility of graphene in different regimesof scattering. . . . . . . . . . . . . . . . . . . . . . . . . . . . 16Table 3.1 ECCOSORB CR-124 epoxy’s typical attenuation. . . . . . . . 40Table 8.1 Characteristic fields for pristine and copper-doped graphene . . 93Table 8.2 Characteristic fields for pristine and copper-doped graphene con-sidering spin-orbit interaction. . . . . . . . . . . . . . . . . . . 94Table A.1 The measured response of RC filters. . . . . . . . . . . . . . . 141Table A.2 The output voltage of Hall sensor versus magnet’s applied current.148Table A.3 Our Allen Bradly resistor calibration table. . . . . . . . . . . . 155xiList of FiguresFigure 2.1 Dirac peak in graphene’s resistivity. . . . . . . . . . . . . . . 7Figure 2.2 Weak localization and weak antilocalizaton in metals and graphene 9Figure 2.3 Band structure of graphene+adatom system. . . . . . . . . . . 14Figure 3.1 Scaled schematic of experimental setup. . . . . . . . . . . . . 24Figure 3.2 The drawing of RC 110H UHV Cryogenic workstation . . . . 26Figure 3.3 Photographs of the magnet frame, before and after winding asuperconducting wire. . . . . . . . . . . . . . . . . . . . . . 27Figure 3.4 Photograph of HTS wires as magnet leads. . . . . . . . . . . 28Figure 3.5 Schematic of wiring in experimental setup. . . . . . . . . . . 29Figure 3.6 Photographs of sample holder and bottom connector. . . . . . 30Figure 3.7 Heater stage. . . . . . . . . . . . . . . . . . . . . . . . . . . 31Figure 3.8 Thermal conductivity of single crystal quartz at different tem-peratures. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32Figure 3.9 Photograph of different samples installed on heater stage: (a)SiC2, (b) SiC3, (c) SiC4. . . . . . . . . . . . . . . . . . . . . 34Figure 3.10 Photographs of sample stage for wire bonding. . . . . . . . . 35Figure 3.11 Photographs of 30 K outer shield. . . . . . . . . . . . . . . . 37Figure 3.12 Photographs of evaporator. . . . . . . . . . . . . . . . . . . . 38Figure 3.13 Photograph of an alkali metal dispenser (SAES Getters) forevaporation of Li. . . . . . . . . . . . . . . . . . . . . . . . . 39Figure 3.14 Photograph of manganin wires covered by ECCOSORB CR-124 epoxy. . . . . . . . . . . . . . . . . . . . . . . . . . . . 40Figure 3.15 Gluing and screwing bottom connector to the magnet frame. . 41xiiFigure 3.16 Placing removable parts. . . . . . . . . . . . . . . . . . . . . 42Figure 3.17 Photograph of cryostat and wobble stick on the top flange ofUHV chamber. . . . . . . . . . . . . . . . . . . . . . . . . . 43Figure 3.18 RGA scan. . . . . . . . . . . . . . . . . . . . . . . . . . . . 44Figure 3.19 Photographs of the experimental setup during cooldown. . . . 46Figure 4.1 Microscope images of exfoliated graphene samples. . . . . . . 49Figure 4.2 [Microscope images of CVD graphene samples. . . . . . . . . 51Figure 4.3 2-probe and 4-probe graphene devices. . . . . . . . . . . . . 53Figure 4.4 Conductivity versus applied gate voltage for monolayer grapheneCVD1. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54Figure 5.1 Li deposition at 3 K on CVD1. . . . . . . . . . . . . . . . . . 58Figure 5.2 Saturated doping in five samples. . . . . . . . . . . . . . . . . 59Figure 5.3 Saturated doping in three different samples before and afterannealing. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61Figure 6.1 Effect of Li deposition on magnetoconductivity of SiC grapheneat T=3 K. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65Figure 6.2 The magnetoconductivity curves of Figure 6.1 versus τ−1B =(4eD/h¯)B and dephasing time. . . . . . . . . . . . . . . . . . 66Figure 6.3 Fitted intervalley time and length versus change of charge car-rier density induced by Li deposition. . . . . . . . . . . . . . 68Figure 6.4 The normalized chi-square value versus different possible Li. . 69Figure 6.5 The inverse mobility and diffusion constant versus change ofcharge carrier density. . . . . . . . . . . . . . . . . . . . . . 72Figure 7.1 Longitudinal resistance Rxx versus temperature T. . . . . . . . 76Figure 7.2 Electronic temperature of SiC1. . . . . . . . . . . . . . . . . 77Figure 7.3 Electronic temperature of SiC4 annealed to 500 K prior tocooldown. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 78Figure 8.1 The effect of 0.002 ML In deposition on graphene sample EXF-BN at 6 K. . . . . . . . . . . . . . . . . . . . . . . . . . . . 84Figure 8.2 More In deposition on EXF-BN after temperature cycling. . . 85xiiiFigure 8.3 SEM images of In clusters on three-layer graphene surface. . . 86Figure 8.4 ToF-SIMS’s positive mode image of EXF1 after deposition. . 88Figure 8.5 Conductivity (σ ) versus back gate voltage (Vbg) for pristineand doped graphene with different adatom coverages for twodifferent samples at 8-12 K. . . . . . . . . . . . . . . . . . . 89Figure 8.6 Magnetoconductivity of graphene flake EXF1 for pristine grapheneand after varying amounts of adatom deposition. . . . . . . . 90Figure 8.7 Dirac peak shift with consecutive Cu depositions on EXF3 at4.4 K. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 91Figure 8.8 Magnetoconductivity of graphene flake EXF3 for pristine grapheneand after varying amounts of copper deposition. . . . . . . . . 92Figure A.1 Drawing of magnet frame. . . . . . . . . . . . . . . . . . . . 117Figure A.2 Photograph of magnet frame. . . . . . . . . . . . . . . . . . . 118Figure A.3 Drawing of aluminum holder for magnet frame. . . . . . . . . 118Figure A.4 Photograph of magnet frame on its aluminum holder. . . . . . 119Figure A.5 Photograph of winding superconducting wire for magnet. . . . 120Figure A.6 Photograph of winded magnet and its solder joints. . . . . . . 121Figure A.7 Drawing of sample holder. . . . . . . . . . . . . . . . . . . . 122Figure A.8 Drawing of bottom connector. . . . . . . . . . . . . . . . . . 122Figure A.9 Drawing of cover plate. . . . . . . . . . . . . . . . . . . . . . 123Figure A.10 Photograph of sample holder, bottom connector, and cover plate.124Figure A.11 Drawing of aluminum part for sample holder. . . . . . . . . . 125Figure A.12 Photograph of aluminum part for sample holder. . . . . . . . 125Figure A.13 Photograph of male and female pin contacts. . . . . . . . . . 126Figure A.14 Photograph of sample holder and its male pins placed insidealuminum part, ready for gluing. . . . . . . . . . . . . . . . . 126Figure A.15 Photograph of final sample holder with its glued male pins. . . 127Figure A.16 Photograph of female pins covered by H77 epoxy in their mid-dle on top of sample holder’s male pins. . . . . . . . . . . . . 128Figure A.17 Soldering wires to female pins under the microscope. . . . . . 128Figure A.18 Photograph of wires soldered to female pins. . . . . . . . . . 129Figure A.19 Gluing female pins with H77 epoxy to the bottom connector. . 129xivFigure A.20 Photograph of twisted wires connected to female pins in bot-tom connector. . . . . . . . . . . . . . . . . . . . . . . . . . 130Figure A.21 Drawing of outer shield ’s adapter. . . . . . . . . . . . . . . . 131Figure A.22 Photograph of gold-plated shield and its adapter. . . . . . . . 132Figure A.23 Drawing of 30 K outer shield. . . . . . . . . . . . . . . . . . 133Figure A.24 Photograph of 30 K outer shield. . . . . . . . . . . . . . . . . 133Figure A.25 Drawing of additional slide part for outer shield. . . . . . . . 134Figure A.26 Photograph of outer shield, shutter and its additional parts. . . 134Figure A.27 Photograph of cryostat and its feedthroughs. . . . . . . . . . . 135Figure A.28 Photograph of manganin wires glued by masterbond epoxy tothe staniless steel body of cryostat. . . . . . . . . . . . . . . . 136Figure A.29 Photograph of manganin wires covered by ECCOSORB CR-124 epoxy. . . . . . . . . . . . . . . . . . . . . . . . . . . . 137Figure A.30 Photograph of black ECCOSORB and white masterbond epoxy. 138Figure A.31 Photograph of RC filters on PCB. . . . . . . . . . . . . . . . 140Figure A.32 The simulated RC filters circuit. . . . . . . . . . . . . . . . . 140Figure A.33 The voltage response of the simulated RC filters. . . . . . . . 141Figure A.34 Placing gold-plated shield and 8” CF. . . . . . . . . . . . . . 143Figure A.35 Gluing and screwing magnet frame to the cryostat’s cold finger. 144Figure A.36 Gluing and screwing bottom connector to the magnet frame. . 145Figure A.37 Photograph of RC filters copper shields. . . . . . . . . . . . . 146Figure A.38 Photograph of copper wires coming from magnet soldered toHTS wires. . . . . . . . . . . . . . . . . . . . . . . . . . . . 147Figure A.39 Circuit map for sensing magnetic field. . . . . . . . . . . . . 148Figure A.40 The output voltage of Hall sensor versus magnet’s applied cur-rent. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 149Figure A.41 Plugging the sample holder with an Allen Bradley in place ofsample. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 151Figure A.42 Mounting the cover plate over sample holder and screwingboth to the bottom connector. . . . . . . . . . . . . . . . . . . 152Figure A.43 Mounting the outer shield. . . . . . . . . . . . . . . . . . . . 153Figure A.44 Installing shutter and its rod for connection to wobble stick. . 154xvFigure A.45 The resistance of Allen Bradley resistor (RAB) vs. silicon diodevoltage (mV) during first cooldown from 77 K to 4.4 K. . . . 155Figure A.46 The temperature of sample measured by Cernox resistor duringthree magnetic field sweep in the range of (-100 mT, 100 mT). 156Figure A.47 Photograph of window flange in the UHV chamber. . . . . . . 157Figure B.1 (a) The inverse mobility and (b) diffusion constant versus changeof charge carrier density induced by Li deposition for of theSiC1,2,3. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 159Figure B.2 The inverse mobility versus change of charge carrier densityinduced by Li deposition for of the CVD1. . . . . . . . . . . 159xviAcknowledgmentsI would like to acknowledge and thank all of those who have contributed to thisproject over the years, beginning with my kind supervisor, Joshua Folk. It has beena great privilege for me to work with him. I would like to thank him for his support,patient guidance and advice he has provided during this project.I also want to thank the current and former members of UBC Quantum De-vices group for their kind support and friendship. Thank you, Julien Renard, MarkLunderburg, Silvia Folk, Matthias Studer, Ebrahim Sajadi, Mohammad Samani,Rui Yang, Oleksandr Rossokhaty, Yuan Ren, Aryan Navabi, Sifang Chen, NikHartman, and Christian Olsen. I specially want to thank Julien Renard, Mark Lun-derburg, Silvia Folk, and Ebrahim Sajadi for helping me in running experiments,understanding the physics behind them and the analyses. I would also like to singleout Julien Renard, for his assistance in building the UHV chamber at the begin-ning of my project. Furthermore, I would like to thank Nik Hartman, MohammadSamani and Saeed Nazari who kindly accept to proofread my thesis.I would like to specially thank Pinder Dosanjh for his great and kind assis-tance in building the experimental set up. I benefited from his incredible level oftechnical skill and knowledge. I also would like to thank my friend Amir HosseinMasnadi for his assistance in building RC filters circuit and its response measure-ment.I would like to thank Prof. Marcel Franz for the inspiration for the heavyadatom experiments and for numerous discussions. In addition, I would like tothank Bart Ludbrook, Giorgio Levy, Pascal Nigge, Yan Pennec, and Profs. AndreaDamascelli, Douglas Bonn, Sarah Burke, Andrew Macdonald, Sebastien Tremblay,and Walter Hardy for the frequent discussions and ongoing collaboration on alkalixviiadatom in graphene. I am really grateful that Prof. Bonn let us use his cryostat andUHV chamber for building our experimental set up.Finally, I would like to thank my family and friends in both Iran and Canadawho helped me in ways I’ll never forget. I would very much like to thank mywonderful parents and beloved sister, to whom I owe endless gratitude for theirunconditional support throughout my life. Lastly, I would like to dedicate thishumble thesis to them.xviiiChapter 1IntroductionGraphene, as a single atomic layer of graphite, is the first known two-dimensional(2D) material. Its 2D structure provides a simple interesting physics such as beinga zero-gap semiconductor with massless Dirac fermions and having valley degreeof freedom in addition to spin degree of freedom. While graphene has a quite lowconductivity at its zero-gap point, known as the Dirac point, the Fermi level ofgraphene can be tuned by doping or varying the gate voltage to create a metal withelectrons or holes charge carriers [2, 3].What makes graphene even more interesting is the possibility of tailoring itselectronic properties by depositing adatoms directly on its surface. Engineeringelectronic properties of graphene via deposition of adatoms has become an activeresearch field in recent years [4, 5]. Many theoretical proposals for modification ofgraphene properties by adatom adsorption exist, especially for metal adatoms. Thepromise of adatom alterations to graphene’s electronic structure has been realizedin some experiments. For example, adsorption of hydrogen [6] and fluorine [7]opened a band gap in graphene [8–10]. Adsorption of fluorine [11] and transitionmetals [3, 12, 13] created local magnetic moments in graphene [14, 15]. Alkaliadatoms have been confirmed to cause charged impurity scattering in graphene[16–18], consistent with theoretical predictions [19–23].However, many important theoretical predictions have not yet been observed,such as induced superconductivity [24–27] and enhanced spin-orbit coupling [28–30]. For example, the theoretically predicted enhancement of dephasing rate by in-1dium induced spin-orbit interaction on graphene [28, 29, 31, 32] was not observedin a recent experiment [33, 34]. This inconsistency between theory and experimentshows the need for further research in this area. Chapter 2 describes the historyof theoretical and experimental research of metal adatom-decorated graphene inmore detail. It also provides the necessary theoretical background for the follow-ing chapters.Transport measurements are an effective tool for probing adatom effects ongraphene electronic properties. The adatom effects on graphene’s Dirac peak in re-sistance, mobility, and magnetoresistance (i.e., weak localization curves) providevaluable information about doping, scattering, valley, and spin related effects (e.g.,possible increasing of the dephasing rate by inducing spin-orbit interaction or mag-netic moments). Temperature can smear these effects. It also can cause clusteringand accumulation of adatoms. Therefore, both adatom deposition and transportmeasurements should be performed at cryogenic temperatures.One of the main obstacles in measuring effects of adatom deposition on graphenetransport is having an experimental setup in which evaporation of adatom and mea-surements can be carried out at low temperature in ultra-high vacuum (UHV). Al-though keeping the sample at cryogenic temperature requires shielding, the hotevaporation source should have direct access to the sample for adatom deposition.Furthermore, the setup should have a magnet with a variable magnetic field forthe purpose of probing charge carrier density by Hall measurements and studyingthe effect of adatoms deposition on dephasing and intervalley scattering throughmagnetoresistance.While magnetoresistance and transport properties of graphene can be measuredat 20 mK in 3He:4He dilution refrigerators [35], evaporation of adatoms in dilutionrefrigerators is challenging, and very few systems offer the type of surface prepara-tion and characterization techniques that are common on higher temperature UHVsystems. To the best of our knowledge, the only report of evaporation of adatoms indilution refrigerators is Ref. [33] in which indium (In) was deposited on grapheneat 5 K followed by measurement at 150 mK. However, their setup seems specifi-cally designed for evaporation of In, with relatively low evaporation temperature.Most in situ transport measurements of adatom-doped graphene have been per-formed from 12 to 77 K [16–18, 33, 34, 36, 37] or at room temperature [38]. Only2a few of these experiments measured magnetoresistance [34]. It is reasonable toassume measuring at 10’s K destroys or thermally smears interesting effects, suchas superconductivity or phase coherence affected by enhancement of spin-orbit in-teraction.To overcome these obstacles, a custom-built UHV setup with a superconduct-ing coil was developed, in which the temperature of graphene device could be keptas low as 3 K during measurements and 4 K during deposition. Chapter 3 ex-plains the design of this UHV cryogenic setup. In addition, more detailed designinformation is provided in Appendix A. We employed this setup to investigate theinfluence of alkali and heavy metals on the transport properties of graphene. Chap-ter 4 provides a description of the methods of our transport measurements and ourgraphene samples.To begin to resolve the inconsistencies between theory and experiment in thisarea, we started with a transport investigation of what is arguably the simplest ofall adatom effects on graphene: charge doping by alkali atoms (Li) deposited un-der cryogenic UHV conditions. While doping in the past transport measurementsof alkali adatoms on graphene was not explored beyond approximately 1% of fullcoverage [16–18] due to limited range of accessible gate voltages, we probed fullcoverage of adatom using the Hall effect by applying a variable perpendicular mag-netic field. Our results demonstrate the critical role of in situ high temperatureannealing in creating reliable adatom-graphene interactions and complete doping[Chapter 5]. High-temperature annealing may solve the problem many groups havefaced in inducing theoretically predicted electronic modifications to graphene byadatom deposition.After doping, we studied the effects of alkali atoms (Li) on long- and short-range scattering in graphene. The general theoretical picture is that each alkalimetal adatom can donate nearly one electron to graphene in a nondestructive waywith minimal effects on the graphene lattice and its electronic states. As a result,these adatoms bond ionically with graphene and act as charged impurity scatteringcenters with a long-range Coulomb interaction [3, 4, 39–44]. While experimentsconfirm that alkali adatoms cause long-range scatterings in graphene [16, 18, 45–47], there is no experimental report that looked for short-range scattering by alkaliadatoms in graphene. Intervalley scattering is a useful probe of short-range scat-3tering. Using magnetoresistance curves, we noticed enhancement of intervalleyscattering by Li deposition. Our results contradict the naive expectation that alkaliadatoms on graphene cannot cause short-range scattering. This is the first exper-imental evidence of short-range scattering from alkali adatoms in graphene andtheir effect on intervalley scattering [Chapter 6]. After studying doping and scat-tering by adatoms in graphene, we looked at other adatoms’ effects like inducingsuperconductivity and spin-orbit interaction.It has been suggested theoretically that alkali metals can enhance electron-phonon coupling in the graphene to the point that makes the graphene a supercon-ductor with critical temperatures of several Kelvin or more [24, 25, 48]. The onlyreport of superconductivity in alkali decorated monolayer graphene in the literaturecame recently from an angle-resolved photoemission (ARPES) measurement of agap in Li-doped graphene, which was interpreted as a superconducting gap corre-sponding to a TC '5.9 K [49]. We searched for this superconductivity in Li-dopedgraphene. However, no signature of superconductivity was observed down to 3 K[Chapter 7].Heavy adatoms are expected to enhance spin-orbit interaction in graphene [28,29]. This enhancement can be detected by increasing of the dephasing rate ingraphene. Increasing of the dephasing rate was observed in graphene decorated bycopper using the weak localization correction to magnetoresistance [Chapter 8].However, inducing magnetic moments by copper can cause a similar effect.4Chapter 2Experimental and TheoreticalBackground: Adatoms onGrapheneThis chapter explains the theoretical backgrounds for our experiments and pro-vides history of theoretical and experimental research. Due to the 2D structure ofgraphene and its unique electronic structure, modification of graphene propertiesby metal adatom adsorption is easily demonstrated in transport measurements [3].Specifically, we are interested in modifications that fall into four different cate-gories:1. Doping (Section 2.3)2. Long-range charged impurity scattering and short-range scattering (Section 2.4and Section 2.5)3. Enhancing electron-phonon coupling and superconductivity (Section 2.6)4. Enhancing spin-orbit coupling (Section 2.7)Before describing the expected electronic modifications due to adatoms, graphene’sHamiltonian (Section 2.1) and weak localization in graphene (Section 2.2) shouldbe explained.52.1 Graphene Hamiltonian and Dispersion RelationThe graphene lattice symmetry causes the electrons in graphene to effectivelybehave as massless fermions with two additional spin-like characteristics calledisospin and pseudospin, in addition to their ordinary spin. While the conductionelectron spin is denoted by the vector of Pauli matrices ~S= (Sx,Sy,Sz), the isospin,which represents A,B sublattice freedom, is denoted by ~Σ = (Σx,Σy,Σz). In addi-tion to isospins, the graphene Fermi level lies near two inequivalent corners of theBrillouin zone, known as K points or valleys (K and K′). The pseudospin, whichrepresents the valley degree of freedom, is denoted by ~Λ= (Λx,Λy,Λz).Graphene’s general Hamiltonian may be written in the following form:H = vF(ΣxΛzpx+Σypy)+U =[HK 00 HK′]+UHK = vF~Σ.~p(2.1)where vF ≈ 106 m/s is the Fermi velocity of graphene, ~p is the momentum mea-sured from the center of a valley. U is the nonmagnetic static disorder term, whichcan include the influence of remote charges that do not break the valley or sublat-tice symmetry, the accounting terms for fluctuations of A/B hopping, and the termswhich generate intervalley scattering [50]. In the absence of impurity scatteringand close to K and K′valleys, the energy dispersion relation is given by [51]:E =±vF | p | (2.2)Figure 2.1 (a) shows the linear band structure of graphene near one of the 6corners of the Brillouin zone, which are known as the Dirac points, based on Equa-tion 2.2. This linearity of the graphene spectrum causes electrons and holes to actas massless Dirac fermions, unlike the massive Schro¨dinger particles in ordinarysemiconductors.The relation between Fermi energy of graphene EF and its charge carrier den-6210௬௫௬௫(a) (c)(b)VBGSi (Bottom Gate)SiO2Graphene-40             -20                0               20              40Figure 2.1: (a) Band structure of graphene near valley points. (b) Schematicgraphene device on silicon oxide/silicon substrate. (c) Example of resis-tivity (ρ) versus applied gate (Vg) voltage for monolayer graphene. Theinsets show movement of the Fermi energy of graphene EF by changingthe gate voltage Vg [adapted from Ref. [52]].sity n is [51]:EF = h¯vFkFkF =√pin(2.3)where kF is the Fermi wavenumber of graphene. Therefore, the position of theFermi level with respect to the band structure can be tuned by changing the chargecarrier density n. One way to change n is to apply a gate voltage Vg to the backof substrate (e.g., doped silicon), while the graphene is placed over a dielectriclike SiO2 [See Figure 2.1 (b)] 1. For example, the graphene/SiO2/Si stack canact as a capacitor, with silicon oxide layer as the dielectric [For further detail seeSection 4.2].1The exact relation between n and Vg will be explained in Section 4.2.7Figure 2.1 (c) explains why we observe a Dirac peak in resistivity versus gatevoltage measurements. The zero density of states at the Dirac point makes itselectronic resistivity quite high. However, the Fermi level of graphene can be tunedby varying the gate voltage to create a high mobility metal with electrons or holescharge carriers.2.2 Weak Localization in GrapheneIn metals, constructive quantum interference between self-crossing paths, in whichan electron propagates in clockwise or counterclockwise directions around a loop,causes weak localization (WL), a slight increase in resistance above the semiclas-sical value at zero magnetic field. WL can be suppressed by a small magnetic fielddue to Aharonov-Bohm phase difference between two paths [See Figure 2.2]. Ina real metal crystal with inelastic collisions due to impurities, electrons, phononsetc., the phase would be lost over time and the interference amplitude is expectedto decay exponentially as a function of time t, as exp(−t/τϕ). This exponen-tial time constant τϕ is referred as the phase-relaxation time. The inverse of thephase-relaxation time is the dephasing rate, τ−1ϕ ,— the rate at which the phase lossevents occur [53, 54]. Its corresponding length, the dephasing length, Lϕ , is equalto Lϕ =√Dτϕ . D is the diffusion constant which is given by [53]:D= τtrv2F2. (2.4)where τtr is the transport time, and its meaning is the lifetime of the momentum.An Aharonov-Bohm phase of order 1 for the perpendicular magnetic field B⊥corresponds to a cutoff area given by L2B = h¯/(eB⊥). The magnetic field destroysphase coherence when this cutoff area is comparable to the phase coherent area,L2ϕ = Dτϕ . Therefore, the phase coherence characteristic field Bϕ , roughly themagnetic field required to destroy phase coherence, is related to the dephasing rateτ−1ϕ through Bϕ = (h¯/4eD)τ−1ϕ [53, 54].In a metal with spin-orbit coupling, the electron’s momentum and spin arecoupled. This causes a pi phase difference and a destructive interference betweenclockwise and counterclockwise paths, which leads to weak antilocalization (WAL),8Figure 2.2: Weak localization and weak antilocalizaton in metals andgraphene [adapted from Ref. [56]].a slight decrease in resistance above the semiclassical value at zero magnetic field.As can be seen in Figure 2.2, WAL also can be destroyed by a magnetic field [55].Due to isospin and momentum coupling in graphene [See Equation 2.1], theisospin must be reversed in order to back-scatter. As a result, there would be api phase difference and a destructive interference between clockwise and counter-clockwise paths which brings up WAL. However, elastic scattering that changesisospin (breaks the chirality) and anisotropy of the Fermi surface in k space (“trig-onal warping”) will destroy the interference within each of the two graphene val-leys in k space. Therefore, the valley-distinguishing disorder strongly suppressesthis WAL. Scattering between valleys, which is also an elastic process, acts to re-store the suppressed interference because two valleys have opposite chirality andwarping. Intervalley scattering allows interference of carriers from different val-leys, which leads to negate the chirality breaking and warping effects. As a result,intervalley scattering returns WL [57] [See Figure 2.2].Taking these effects together, WL in graphene is governed by three scatteringrates: two represent scattering between, τ−1i , or within, τ−1∗ , band structure valleyswhich are called intervalley and intravalley rates; the third, τ−1ϕ , is the conventionaldephasing rate well-known from WL studies in metals. These three rates are relatedto their corresponding fields through τ−1ϕ,i,∗ = (4eD/h¯)Bϕ,i,∗ where the diffusion9constant in graphene D may be calculated using the formula [58]:D=σpi h¯vF2e2√pin. (2.5)Bϕ,i,∗ can be extracted by fitting magnetoconductivity curves to the WL formfor graphene [59]:∆σ(B⊥) = σ(B)−σ(0) = e2pih[F(BBϕ)−2F( BBϕ +B∗+Bi)−F( BBϕ +2Bi)]F(z) = ln(z)+ψ(1z+12)(2.6)where B is magnetic field, ψ(x) is the digamma function.The dephasing rate at low temperatures is dominated by the linear-in-temperaturecontribution due to electron-electron (e-e) interactions [54, 57]. In the case ofgraphene with spin impurities, an additional temperature-independent term wouldbe added [60]. The linear term of the dephasing rate has been calculated to be[54, 60]:τ−1ϕ =kBln(g/2)h¯gT (2.7)where g= σh/e2.2.3 Adatoms’ Doping of GrapheneAn adatom is an adsorbed atom that lies on a crystal surface (in our case graphene).Regardless of their type, adatoms usually induce charge doping in graphene. Thisdoping changes the charge carrier density n in graphene, which can be measuredwith the shift of the Dirac peak. If an adsorbate donates electrons (holes) tographene, the Dirac peak shifts to more negative (positive) gate voltages. Mostmetals donate electrons to graphene, making it n-doped [4, 43, 44].The Dirac peak shift in gate voltage is a useful probe of charge carrier densityfor mild doping, but is ineffective at higher densities when the Dirac peak movesout of the range of accessible gate voltages, and on graphene samples without agate. Induced charge density can also be monitored using the Hall effect, away10from the Dirac point 2.Although the induced carrier density ∆n can be determined by Dirac point shift,the density of adatoms on the surface nimp cannot be directly measured. The ratiobetween the two is η , the net charge transferred per adatom (nimp = ∆n/η) 3.2.4 Long-range and Short-range Scattering in Graphenedue to AdatomsIn addition to doping, adatoms also affect the scattering of electrons in graphene.Adatoms can modify scattering in graphene in different ways. There is a generalconsensus, from both experiment and theory, that each of the alkali metals or alka-line earth metals adatoms (groups I-II of the Periodic Table) can donate nearly oneelectron to graphene in a nondestructive way with minimal effects on the graphenelattice and its electronic states. As a result, these adatoms bond ionically withgraphene and act as charged scattering centers with long-range Coulomb interac-tion [3, 4, 16, 18, 39–47]. In contrast, the transition, noble, and group IV metalsadatoms can cause strong hybridization between their own and the graphene elec-tronic states, making covalent bonds, disturbing the graphene lattice and causingshort-range scattering [3, 4, 43, 44]. Group III metal adatoms are considered in be-tween these two groups due to their mixed covalent and ionic bonding [3, 4, 43]. Asshown experimentally for thallium-doped graphene, the group III metal adatomsact as both long-range and short-range scatterers [61]. In Chapter 6 of this thesis,we will show that this classification for the nature of bonding of different groups ofthe Periodic Table is a bit naive, especially about alkali metals. For now, we focuson long-range (LR) versus short-range (SR) scattering in graphene.At cryogenic temperature, the scattering due to phonons is insignificant. There-fore, there are two main mechanisms for scattering in graphene: long-range Coulomb2We will describe these two methods of measuring charge carrier density in Section 4.2.3In a more comprehensive picture, nimp=∆n/η also reflects the screening properties of graphene.In a case that the charge is distributed non-uniformly, the average potential may be rather differentthan the potential one expects if the charge is distributed uniformly. For example, [19] predictsthat ∆n is a function of nimp, dielectric constant of substrate and the distance between impurity andgraphene plane, even though the impurity charge is unity (Z = 1). Interestingly, the function in [19]converges to a constant at large charge carrier densities (which is our case) and make ∆n = nimp avery good estimate. Anyway, if the screening is accounted in η , the relation would be exact.11interactions for charged impurities (whether deposited as adatoms on graphene oralready placed on its substrate) [16, 18, 19, 21, 22, 62] and short-range interactionsdue to neutral defects [63], ripples [16, 64], cracks or boundaries in the graphenesheet [65], and covalent bonding of adatoms with graphene (for example in dilutefluorinated graphene [66] or indium [34], and nitrogen [67] doped graphene).2.4.1 Long-range Scattering due to AdatomsLong-range scattering in graphene due to charged impurities results in a finite con-ductivity given by [16, 19, 21, 22, 62]:σc = neµc =Cennimp,cµc =Cnimp,c(2.8)where C is a constant and nimp,c is the charged impurity density (i.e., density ofCoulomb long-range scatterers). Ref. [19] found C = (2e/h)(1/G(2rs)) whereG(2rs) is an analytical function of the dimensionless interaction strength in graphene,which is:G[x]x2=pi4+3x− 3pix22+x(3x2−2)arccos[1/x]√x2−1 (2.9)and rs = 2e2/(h¯vF4piε0(k1 + k2)) is the coupling constant, 4 for graphene sand-wiched between two dielectric materials with dielectric constants k1 and k2. In thers formula, vF is the bare Fermi velocity (i.e., the Fermi velocity for ε =∞), whichis vF = 0.85×106 m/s.Since we will use graphene samples on SiO2 or SiC substrates in this project,we calculate C for these two cases. For graphene on a SiO2 substrate, using thedielectric constants of the vacuum (kvac = 1) and SiO2 (kSiO2 = 3.9), we find rs ≈0.8 and C = 20e/h≈ 5×1015V−1.s−1. At least three different dielectric constantshave been suggested for SiC: (1) kSiC = 43± 16 [69], (2) kSiC = 9.66 [70, 71] for6H-SiC, and (3) kSiC = 13.52± 0.04 which was first measured for 4H-SiC [68]but has recently been used for 6H-SiC as well [61]. While the first value (kSiC =4Another name of this parameter is the fine structure constant. This parameter determines thestrength of the Coulomb coupling [68].1243±16) is considered overestimated [61], the other two values are commonly used.Using the dielectric constants of the vacuum (kvac = 1) and SiC (kSiC = 9.66−13.52) gives rs ≈ 0.35−0.4 and C ≈ (8.5±0.5)×1015V−1 · s−1.The diffusion constant due to Coulomb long-range scattering depends on bothcharge carrier density n and charged impurity density nimp,c. Using Equation 2.9and Equation 2.5, D is given by [62, 72]:D= τtrv2F2=εFev2FCnimp,cv2F2=εFC2enimp,c=Ch¯vF√pin2enimp,c(2.10)where τtr is the transport time and εF is the Fermi energy Short-range Scattering due to AdatomsAnother type of scattering is short-range scattering. The short-range scatteringcenters impose a potential of the form [51]:U =Ue f fΣNn=1δ (Rn− r) (2.11)where N and Rn are the number and place of scattering centers, respectively. In thecase of adatoms that cause short-range scattering, two additional terms would beadded to the graphene Hamiltonian: Had for the adatom and Hc for the coupling be-tween adatom and graphene, which allows electrons to tunnel between the adatomand its neighboring carbon sites. As can be seen in Figure 2.3, Ead is an on-siteenergy of the electron in the unperturbed adatom which comes from Had . Hc in-troduces tad−gr as the hopping amplitude between the adatom and carbon atoms ingraphene. In this case, Ue f f = t2ad−gr/ | EF −Ead | where EF is the Fermi energy ingraphene. Therefore, if there are impurity states (of the unperturbed adatom) closeto the Fermi level inducing a large Ue f f , the short-range scattering becomes sig-nificant. This strong short-range scattering has been also called resonant scattering[51, 61, 73–75].Using the nonperturbative self-consistent Born approximation (SCBA) and mod-eling of resonant scatterers with disks of radius R0 (of the order of the size of the5We will use this formula to see if change of diffusion constant due to adatom deposition followsthe long-range theory or not. For example, see Figure 6.5 (b).13Figure 2.3: Band structure of graphene+adatom system [adapted from Ref.[76]]. While horizontal dashed line indicates the Fermi level of dopedgraphene, the red line shows the parabolic-shaped band of adatom.The term tad−gr indicates the hopping amplitude between adatom andgraphene.primitive lattice vectors) such that the electron wave function is zero for r < R0,results in a conductivity for kFR0 << 1 [14, 51, 63, 65]:σs = neµs =2e2pihnnimp,sln2(kFR0) =2e2pihnnimp,sln2(R0√pin)µs =2epih1nimp,sln2(R0√pin)(2.12)where nimp,s is the density of short-range scatterers. It should be noted that unlikethe equivalent Equation 2.8, which describes long range scattering, the applicationof Equation 2.12 is limited. It is shown experimentally that as temperature de-creases 6 and/or nimp,s increases, localization effects become important and Equa-tion 2.12 is inapplicable 7 [14, 77].6For example, when temperature of fluorinated graphene decreased to 5 K, Equation 2.12 wasreported inapplicable [77].7Long-range scatterers are in the Drude-Boltzmann diffusive transport regime in which localiza-14In contrast to strong short-range (resonant) scattering, when the strength ofscattering potential Ue f f is finite and small enough to treat the short-range scatter-ing potential as a perturbation, the first Born approximation (Fermi’s golden rule)can be used to calculate the scattering matrix and conductivity. This is on contrastto the nonperturbative self-consistent Born approximation (SCBA) which usuallyapplies for conductivity in the case of strong short-range scattering. Weak short-range scattering gives rise to a conductivity that is independent of charge carrierdensity n and µ ∝ 1/n [51, 63, 65, 78, 79]. In this case, the conductivity andmobility have the following form [65, 78]:σs = neµs =8e2hh¯2v2Fnimp,sU2e f fA2u.c.µs =8enhh¯2v2Fnimp,sU2e f fA2u.c.(2.13)where Au.c. =√3(2.46A˚)2/2 is the graphene unit cell area [See Table 2.1]. Wewill use this formula and weak short-range scattering regime in Chapter 6 to studyscattering due to alkali adatoms.Considering the relations for both types of scattering together, the inverse ofmobility in the long-range scattering regime has a simple linear relation with thecharged-impurity density, through the equation 1/µ = nimp/C independent of n.However, the inverse of mobility in short-range scattering depends on n as well(either directly in weak short-range scattering or logarithmically in strong short-range scattering) and the simple linear relation with nimp does not hold [16, 79,80]. If there is both long-range and short-range scattering in graphene, the totalconductivity and mobility can be found through Matthiessen’s rule [16, 51, 63]:ρ =1σ=1σc+1σs⇒ 1µ=1µc+1µs(2.14)Table 2.1 summarizes the conductivity and mobility formulas for differentregimes of scattering that were introduced in this section.tion effects are not important [19].15Table 2.1: The conductivity and mobility of graphene in different regimes ofscattering.Type of scattering Conductivity (σ = neµ) Mobility (µ)LR (charged impurity) σc =Ce nnimp,c µc =Cnimp,cStrong SR (resonant) σs = 2e2pihnnimp,sln2(R0√pin) µs = 2epih1nimp,sln2(R0√pin)Weak SR σs = 8e2hh¯2v2Fnimp,sU2e f fA2u.c.µs = 8enhh¯2v2Fnimp,sU2e f fA2u.c.LR+SR 1σ =1σc +1σs1µ =1µc +1µs2.5 Intervalley Scattering in GrapheneSection 2.4 described how the change of mobility due to changing densities ofadatoms can help us to understand their scattering type. However, when both long-and short-range scattering are produced by an adatom, it is hard to discern bothseparately, especially if one is dominant. As we will explain in the following, theintervalley scattering rate, which is the rate of scattering between two valleys, isan efficient way to isolate the effects of short-range scattering. The intervalley rateτ−1i and its corresponding length, intervalley length Li, can be obtained from weaklocalization fits [See Section 2.2]. The type of scattering (long- or short-range) canbe determined by comparing the measured values of τ−1i with Equation 2.15 andEquation 2.17 that we will introduce in this section.According to Fermi’s Golden Rule, the impurity-induced transition rate frommomentum state k to state k′ is related to the 2D Fourier transform (FT) of theimpurity potential. As a result, the intervalley scattering rate has the same de-pendence. The 2D FT of the long-range Coulomb potential of a single chargedimpurity, located at a distance d from the graphene sheet, is 2pie2e−qd/(q4piε0)where q = k− k′ and e is the magnitude of the electron charge. Therefore, theFourier spectrum of Coulomb potential is peaked around small wave numbers. In-tervalley scattering requires momentum transitions between the two Dirac cones,which are separated in momentum by K = |K−K′| ≈ 1.7 A˚−1. Plugging this largevalue as the wave number into the mentioned FT formula for the Coulomb poten-tial produces a small intervalley scattering rate [72]. However, the FT of the deltafunction potential for short-range scattering is constant and its resulting intervalley16scattering rate can be significant.The intervalley rate due to long-range Coulomb scattering can be found throughthe following formula [72]:1τi= 2βnimp,cεFh¯3v2Fe44ε20K2e−2Kd (2.15)where β is a constant that depends on screening and effective Bohr radius; it isestimated to be 0.12 in graphene (β = 1.9 in the case of unscreened impurities), εFis the Fermi energy, and d is the charged impurity distance from the graphene plane.As τi ∝ 1/(nimp,cεF) [See Equation 2.15] and D ∝ εF/nimp,c [See Equation 2.10],the intervalley length Li =√Dτi is given by [72]:Li ≈ AeKd/nimp,c (2.16)where A= 2h¯vFKε0√h¯C/(βe)/e2 is a constant.If impurities (in our case adatoms) produce short-range potential with ampli-tude of Ue f f as described in Equation 2.11, in addition to Coulomb long-rangepotential, Equation 2.15 will be revised to the following form [75]:1τi=32nimpεFpi2h¯3v2F| Γ(γ+1+ irs)Γ(2γ+1)|4 FZU2e f fa44(1−2r2s )Fz = (2aεFvF h¯)2√1−4r2s−2(2.17)where a= 2.46 A˚ is the graphene lattice constant, γ =√0.52− r2s , and rs is the cou-pling constant introduced in Section 2.4. We will use Equation 2.17 in Chapter 6to explain the enhancement of intervalley scattering in graphene by Li deposition.In addition to long- and short-range scattering, electron-phonon interaction canin principle induce intervalley scattering. However, it is irrelevant to the intervalleyscattering in our experiments because the phonons with momentum q = K neces-sary for intervalley scattering have energy ∼160 meV and therefore are not sig-nificantly populated even at room temperature [81–83] [See Section 6.2 for moredetails].172.6 Enhancement of Electron-Phonon Coupling andInduced Superconductivity in Graphene by AlkaliAdatomsBeside doping and scattering, another possible impact of adatoms is changingelectron-phonon interaction in graphene. Alkaline adatoms (alkali metals or alka-line earth metals) are expected to increase electron-phonon coupling in grapheneto the point that superconducting critical temperatures of several Kelvin or moreare achieved [24, 25]. The enhancement of electron-phonon coupling is due toboth charge transfer from the alkali to the graphene, leading to higher electronicdensity of states in the graphene, as well as (predicted) changes to the deformationpotential and phonon frequency [3, 24, 84].It has been known since the 1960s that alkaline atoms intercalated into bulkgraphite—yielding compounds such as C8K [85, 86], C8Rb [85, 87], C8Cs [85],C6Ca [88–90], or C6Sr [91] and metastable high-pressure phase C2Li [92]—inducesuperconductivity. Recent interest in the topic has focused on questions of howthis effect will scale to thinner and thinner graphite layers, down to the single-layerlimit of graphene, or with different choices of dopant adatoms. Superconductivityhas been reported in few-layer graphene and graphene laminates doped with Li,Ca, or K via intercalation [93–98].We were specifically interested in Li-induced superconductivity in monolayergraphene which is theoretically predicted by Ref. [24], [48] and [84] to have acritical temperature in the range of Tc=5.1-10.33 K. Ref. [94] and [97] explic-itly checked for, and found no sign of, Li-induced superconductivity in bilayergraphene down to 0.8 K and graphene laminate down to 1.8 K. The only experi-mental report of superconductivity in Li-decorated monolayer graphene in the liter-ature came recently from an angle-resolved photoemission (ARPES) measurementof epitaxial SiC-graphene, onto which Li adatoms were deposited by physical va-por deposition at cryogenic temperatures, with a Tc of 5.9 K inferred from theirobserved gap [49].One of the challenges moving forward in this area is the difficulty of compar-ing experiments performed using different forms of graphene, different depositiontemperature, different substrates, and/or different alkaline adatoms, to each other18and to theoretical predictions. Even for a given adatom species like Li on singlelayer graphene, deposited adatoms may remain on top of the graphene sheet atits interface with vacuum [99, 100], or they may intercalate underneath betweenthe graphene and its substrate [101–103], depending on the preparation condi-tions. Furthermore, the variety of experimental approaches to preparing alkali-on-graphene samples has made it hard to integrate input from multiple groups spe-cializing in different techniques such as scanning tunneling microscopy (STM)[104–106], low-energy electron diffraction (LEED) [93, 104, 106, 107], ARPES[49, 90, 93, 99, 104, 106, 107], transport [94, 95, 97], etc.In our transport experiments, we do not have any way to probe electron-phononenhancement. However, we will look for theoretically predicted superconductivityin Li-doped graphene, emulating as closely as possible the conditions in Ref. [49],by monitoring its resistance as a function of temperature [Chapter 7].2.7 Enhancement of Spin-orbit Interaction by HeavyAdatoms in GrapheneHeavy adatoms are predicted to introduce a spin-isospin (effectively spin-orbit)coupling in graphene of the form [50]:HSO = λKMΣzSz+λBR(ΣxSy−ΣySx) (2.18)The first term in the Hamiltonian is referred to as the Kane-Mele (KM) term, af-ter the names of Charles L. Kane and Eugene J. Mele. It is sometime also calledthe intrinsic term, because it can exist intrinsically (without any adatom or extrin-sic effect) in graphene and introduce a gap of ∆SO = 2λKM. However, this gap isvery small with energies in the range 1-50 µeV in pristine graphene [108–112].The second term in the Hamiltonian is referred to as Bychkov-Rashba (BR), afterthe names of Yu A. Bychkov and Emmanuel I. Rashba, and can be generated ex-trinsically by breaking of the mirror (z/-z) symmetry in the graphene plane [50].While Kane-Mele spin-orbit coupling in graphene conserves the Sz spin compo-nent, Bychkov-Rashba spin-orbit interaction causes flipping of Sz. In the case ofadatom induced spin-orbit interaction, both λKM and λBR depend on density and19species of adatoms [28, 113].Now, let us explain the mechanism of enhancement of spin-orbit interactionin graphene by heavy adatoms deposition. At a qualitative level, electrons fromgraphene tunnel onto the adatoms, feel enormous spin-orbit coupling, then tunnelback to the graphene sheet, bringing part of the spin-orbit modification with them.It has been suggested that adatoms may enhance intrinsic (Kane-Mele) spin-orbitcoupling to the point the graphene becomes a quantum spin Hall (QSH) insula-tor by opening a gap of ∆SO = 2λKM and introducing edge states. QSH states,including gapless edge states that are protected from elastic backscattering and lo-calization by time-reversal symmetry, realize a topological phase that depends onlyon global topology and not on local details, such as disorder. To realize this effectexperimentally, adatoms should have the following characteristics: (1) they shouldbe nonmagnetic (to preserve time-reversal symmetry) and (2) they should favor thehollow position (i.e. the site above the center of the hexagonal ring) in the graphenesheet (to most effectively mediate the spin-dependent second-neighbor hoppingspresent in the Kane-Mele model, while simultaneously avoiding larger compet-ing effects such as local sublattice symmetry-breaking generated in other cases).While these two conditions are necessary, they are not sufficient conditions. Thereare other conditions that should cause adatoms mediate Kane-Mele spin-orbit in-teraction in graphene which dominate over the induced Bychkov-Rashba spin-orbitinteraction [28, 29].Heavy adatoms generically mediate both Kane-Mele and Bychkov-Rashba spin-orbit interactions in graphene. However, their orbital contribution to graphene (forexample whether the adatoms’ outer-shell electrons derive from p orbitals or d or-bitals) and their position on graphene are significant factors in determining whichtype of spin-orbit interaction will dominate. For example, adatoms with active elec-trons residing in p orbitals located in hollow positions produce a Kane-Mele type ofspin-orbit interaction [28, 114]. However, adatoms placed in the top position (i.e.above a carbon atom) with active electrons in p orbitals induce a Bychkov-Rashbatype of spin-orbit interaction [114].It is theoretically predicted that indium (In) and thallium (Tl), both of whichhave partially filled p shells, favor the hollow position. A modest 6% coverageof indium (In) and thallium (Tl) produce dominant Kane-Mele spin-orbit coupling20with λKM =3.5 and 10.5 meV, respectively [28, 31, 32]. Osmium (Os) and iridium(Ir), both of which locate in the hollow position and have partially filled d shells,are also predicted to produce dominant Kane-Mele spin-orbit coupling on the orderof λKM =100 meV [29]. However, gold (Au) adatoms deposited in the top positionof graphene with active electrons residing in d orbitals results in a Bychkov-Rashbaspin-orbit coupling with a predicted strength ranging from λBR =10 meV [115] toλBR =100 meV [116]. In the case of 1% coverage of copper (Cu) adatoms placedin top position on graphene, it is predicted that both of copper’s p and d orbitalcontributions are equally important to its induced spin-orbit coupling with strengthof λKM =9 meV and λBR =30 meV [113].There is a discrepancy between theory and experiment in heavy adatom in-duced spin-orbit coupling 8. For example, the theoretically predicted enhance-ment of spin-orbit interaction on graphene by indium [28, 31, 32] has not beenobserved experimentally [33, 34]. In Ir-decorated graphene, no signature of thetheoretically predicted spin-orbit coupling induced QSH effect [29] has been ob-served [117]. An experimental report describing Au adatom on graphene shows achange of spin lifetime with increasing Au coverage, measured by non-local spininjection [118]. Supposing Rashba spin-orbit coupling, their measurement leads tospin-orbit strength of the order of λBR =0.2-0.3 meV, which is much smaller thantheoretical predictions [115, 116].As we will explain in Chapter 5 of this thesis, this inconsistency between theoryand these experiments probably occurred due to lack of reliable interaction betweengraphene surface and adatom in the experiments. Our measurements in Chapter 5will demonstrate that in situ high temperature annealing is necessary for creatingthis reliable adatom-graphene interaction.One way of observing spin-orbit interaction experimentally is non-local mea-surements (i.e. sending current through two contacts and measuring non-local volt-age at two other contacts at some distance from current pads), which was usedfor probing spin-orbit interaction in copper-doped graphene [119]. However, the8Here we limit ourselves to reviewing the experimental reports about spin-orbit interaction ingraphene before and after adatom deposition on the surface of graphene. There are other experimentswhich look at enhancement of spin-orbit interaction by intercalation of these heavy adatoms betweengraphene and substrate or by placing graphene on a substrate of one of these heavy adatoms.21non-local signal may have a valley or temperature origin and not necessarily spin[117, 120].In addition to non-local measurements, weak localization can be used for de-tection of spin-orbit interaction. Unlike non-local measurements, weak localizationmeasurements can differentiate between spin and valley. For graphene with spin-orbit coupling, the WL contribution changes from Equation 2.6 to the followingform [50]:∆σ(B⊥) =− e22pih[F(BBϕ)−2F( BBϕ +B∗+Bi)−F( BBϕ +2Bi)−2F( BBϕ +BBR+BKM)+4F(BBϕ +B∗+Bi+BBR+BKM)+2F(BBϕ +2Bi+BBR+BKM)−F( BBϕ +2BBR)+2F(BBϕ +B∗+Bi+2BBR)+F(BBϕ +2Bi+2BBR)](2.19)where BKM,BR = (h¯/4De)τ−1KM,BR, with two scattering rates: a scattering rate re-lated to Kane-Mele (KM) spin-orbit coupling (τ−1KM) and a scattering rate relatedto Bychkov-Rashba (BR) spin-orbit coupling (τ−1BR ). These two scattering rates arerelated to the Hamiltonian of Equation 2.18 by [50]:τ−1KM = τ−10 (λKMεF)2 =1D(vFλKMεF)2τ−1BR =2τ0λ 2BRh¯2=2Dλ 2BRv2F h¯2(2.20)where τ0 = 0.5τtr = D/v2F [See Equation 2.10] is the scattering time. When BRspin-orbit coupling is negligible, Equation 2.6, which is obtained by neglectingspin-orbit coupling, can be used with a modified definition of the dephasing char-acteristic field as Bϕ −→ Bϕ + BKM to consider the influence of the KM spin-orbit [50]. This means a modified definition of the dephasing rate as τ−1ϕ /D0 −→(τ−1ϕ + τ−1KM)/D, where D0 and D are diffusion constants before and after induc-ing spin-orbit interaction, respectively. This increasing of dephasing rate by en-hancement of spin-orbit interaction which is theoretically predicted for In and Tl[28, 31, 32] should show itself in widening of the WL graph [See Figure 2.2].22Chapter 3UHV Cryogenic Evaporation andMeasurement ChamberOur adatom-based experiments depended on an apparatus in which we could cleana graphene sample surface, evaporate controllable densities of adatoms, then per-form a transport measurement, all in situ without breaking vacuum or even let-ting the sample heat up above cryogenic temperatures. We achieved this with acustom-built setup, which will be described in this chapter. Section 3.1 providesan overview of our experimental setup. Then, the following sections (from Sec-tion 3.2 to Section 3.12) give a brief description of different parts of setup, theirconstruction, and assembly. Finally, Section 3.13 describes the cooldown and op-eration of setup. In addition to this chapter, Appendix A goes into further technicaldetails about the experimental setup.3.1 Overview of Experimental SetupFigure 3.1 includes a schematic of the UHV chamber used for this experiment, in-cluding each of the critical elements. As can be seen in Figure 3.1 (a), there is acryogenic stage on the top flange of the UHV chamber for installing our graphenesample [For more details about the cryostat, see Section 3.2]. Figure 3.1 (b) showsa close-up view of sample stage. The sample sits at the center of a superconduct-ing coil that could be energized to 100 mT [For more details about this magnet23Figure 3.1: (a) Scaled schematic of experimental setup; dashed line illustratesthe walls of UHV chamber. W: wobble stick. (b) A close-up view of thesample stage in panel (a); S: sample, D: diode, C: cernox.24and its leads, see Section 3.3 and Section 3.4]. The frame of this magnet, plus acover plate, act as a 4 K shield. The sample holder contains a graphene samplewhose contacts are connected to the male pins in the sample holder. The sampleholder’s male pins are plugged to the female pins of the bottom connector [Formore details about the bottom connector and different types of sample holder, seeSection 3.5, Section 3.6, and Section 3.7]. The sample holder and bottom con-nector are screwed to the magnet frame, which itself is glued and screwed to thecold finger. A silicon diode (Lakeshore DT-670B-SD) and a CernoxTM resistancesensor (CX-1050-BG-HT) are attached to the cold finger and sample holder, re-spectively, to monitor their temperatures [See Section 3.8]. An additional 30 Kshield can be closed using a mechanical shutter before and after adatom evapo-ration [See Section 3.9]. A thermal evaporator is located underneath the samplestage on the bottom flange to evaporate adatoms onto the graphene surface by driv-ing current through it [See Section 3.10]. In the next sections, we will explain eachof the mentioned parts. Most of these custom-made components were designedusing “SolidWorks” software and made in the Physics machine shop.3.2 Liquid Helium Flow CryostatWe used a liquid helium (LHe) flow cryostat, “RC 110H UHV Cryogenic work-station” made by “CRYO Industries of America, Inc.” as shown in Figure 3.2. Thesetup was built around this cryostat after some revisions 1. The cryostat’s coldfinger is a copper stub, which contains LHe in its interior during cooldown.3.3 Superconducting MagnetOne of the essential parts of the setup is a copper magnet frame, which acts as botha magnet frame and a part of the 4 K shield [See Figure 3.1 (b) and Figure 3.3 (a)].A series of screw holes were placed on the top of the part to allow two other coppercup-shaped parts (bottom connector and sample holder) to be screwed to this part.The magnet frame itself was glued and screwed to the cold finger. Superconduct-ing wire was wound on this frame (465 turns) using a winding machine. A two-1The length of the 4.62” to 2.75” CF neck adapter were changed from 5.88” to 4.11” and twoadditional electrical feedthroughs were added.2510 pin electrical feedthrough helium vent with 25 klein flange  quick disconnect for transfer line/work station separation  1.33 conflat blank port  4.62 conflat flange 30 K vapor cooled radiation shield 2.75 conflat flange heater cold finger Figure 3.2: The drawing of RC 110H UHV Cryogenic workstationcomponent, thermally conductive, electrically insulating epoxy named EPO-TEKH77 was used for filling space between superconducting wire turns and making agood thermal connection to help cooling the magnet wires. After finishing the wirewinding, two pieces of 22 AWG kapton insulated silver plated copper wires weresoldered to the two ends of superconducting wire [See Figure 3.3 (b)]. Further de-tails about the magnet frame and the winding process are provided in Section A.1and Section A.2.After building the magnet, its magnetic field to current ratio (B/I) was mea-sured using a linear Hall effect sensor as B/I = 18 mT/A which is consistent withour theoretical estimation based on magnet geometry [See Section A.10]. The ho-mogeneity of magnetic field B across the sample area was also characterized bythe linear Hall effect sensor (The variation of B across the sample was less than26Figure 3.3: Photographs of the magnet frame, (a) before and (b) after windinga superconducting wire. The superconducting wire’s solder joints to themagnet’s copper wire leads can be seen in the photograph.0.08 mT/A).3.4 Magnet LeadsFor magnet leads, two 22 AWG copper wires coming from a 4-pin feedthrough en-ter under the 30 K shield and are soldered to the high-temperature superconducting(HTS) wires. Two 4 mm width HTS wires were glued underneath the gold-plated30 K shield using Masterbond epoxy [See Figure 3.4 and Figure 3.5].Later HTS wires were soldered to 22 AWG copper wires coming from the su-perconducting magnet [See Figure A.38]. Thus, each magnet lead contains: a cop-per feedthrough+copper wire+HTS+copper wire. It is known that HTS wires arepoor thermal conductors; however, our HTS wires have a layer of copper and sil-ver with 44 µm thickness. It is important to remember that we thermally anchoredthe HTS strips with Masterbond epoxy to the stainless steel body underneath thegold-plated shield, to let cold helium gas, which is going to exhaust, cool down theHTS strips efficiently 2. Based on the cryostat manual, the gold-plated shield hasa temperature of 30-40 K. Therefore, the HTS strip should be much colder than 30K. But for simplicity, let us consider 30 K and calculate how much LHe will boil2Note that the liquid helium path and helium gas exhaust are separate from the chamber vacuum.27Figure 3.4: Photograph of HTS wires as magnet leads.due to this configuration.The resistivity of copper in the range of 4 to 10 K is around ρ=10−10 Ω.m. Thelength of the HTS wires is 16 cm, considering the width of 4 mm and thickness of44 µm and using R = ρl/A, where l is the length and A is area, the resistance ofeach wire is about 10−4 Ω. Now, there are two sources of thermal power. One isthe electrical power RI2, due to passing current I from the magnet leads. Consid-ering a maximum current of 10 A 3, this power is 0.01 W. The second power is theconductance power between room temperature and the cryogenic temperature part,which may be found with (L/(2R))× (T 2hot−T 2cold) where L= 2.44×108 W.Ω/K2,is the Lorenz number [121]. Considering Thot=300 K and Tcold=30 K, this poweris 0.11 W. In total 0.12 W thermal power comes through the magnet leads. Con-sidering the low latent heat of liquid helium vaporization, which is only about 2.6kJ/l or 0.72 watt-hour per liter, a heat input of 0.12 W will boil away 0.2 liters ofliquid helium in an hour.3In reality, we did not use a current more than 6 A.28Figure 3.5: Schematic of wiring in experimental setup.293.5 Sample Holder and Bottom ConnectorFigure 3.6: Photographs of (a) sample holder with its glued male pins, and(b) bottom connector with its twisted wires connected to female pins.Figure 3.1 (b) shows how these different parts fit together.The sample holder is a cup-shaped copper piece which was designed to placea graphene sample in the center of the magnetic field produced by the supercon-ducting magnet. Each of sample’s contacts is connected by a gold wire to a malepin glued to a hole in the bottom of sample holder. The sample holder allowsthe graphene device to be easily electrically connected to our measurement equip-ment by plugging its male pins to the female pins on another cup-shaped copperpiece on the bottom. We call this bottom socket, the bottom connector [See Fig-ure 3.1 (b) and Figure 3.6]. The female pins in the bottom connector are solderedto some twisted copper wires, which are connected to the measurement equipmentthrough other wires [See Figure 3.5]. The sample holder and bottom connector,which are screwed to the magnet frame, are also designed to make the graphenesample thermally anchored to the cold finger through the magnet frame [See Fig-ure 3.1 (b)]. Samples were glued to the sample holder with a UHV compatible,high temperature tolerant copper paste (TR-890 M from “Tanaka Kikinzoku Inter-national K.K.”) and H20 silver epoxy was used for connecting wires from samplesto the male pins. Further details about sample holder and bottom connector can befound in Section A.3 and Section A.4. In the next two sections, the design of two30Pins Quartz Plate Graphene Gold  wire Copper  Stage Figure 3.7: Pre-annealing stage, showing 9 male pins and grahene on SiCchip glued to end of quartz plate with thermocouple attached to pinsTC+ and TC-.additional sample stages will be explained.3.6 Heater StageFor some graphene samples, we used a customized stage that enabled annealingoperations close to 1000 K prior to cryogenic adatom deposition. A revised sam-ple holder was designed for this purpose. The sample holder still had the samestructure; however, it had two parts. The bottom part for the sample holder, whichwe call the custom heater stage, was separated from the top part (which now lookslike a cup without a bottom) to give more freedom for loading samples. After asample is placed in the bottom part, it is screwed to the top part [See Figure 3.7].The main challenge of making a heater stage is that the area around the graphenesample which contains glued gold wires and pins covered by epoxies cannot toler-ate more than 450 K. This raises the need for the thermal separation of the sampleand the sample stage. However, sample and sample stage should have a good ther-mal connection at cryogenic temperature to allow the sample cool down to 3 K. To31Figure 3.8: Thermal conductivity of single crystal quartz at different temper-atures. The data points are taken from Refs. [122], [121], and [123].satisfy these two conditions, we have to separate the sample and the sample stageby a material that is a very bad thermal conductor at T ≥ 300 K and a good thermalconductor at cryogenic temperatures (T = 3−4 K) 4. Single crystal quartz has sucha characteristic [See Figure 3.8].Let us calculate the thermal conductivity of a single crystal quartz piece suit-able for our dimensions. Thermal conductivity of single crystal quartz parallel to itssurface is 9.5 W/m.K at 300 K [124] and 10.7 W/m.K at 323 K [123]. We choose 10W/m.K for simplicity. The rate of heat flow Q˙ resulting from a temperature gradient∆T , in a material of thermal conductivity k, cross-section A, and length L, is givenby Q˙ = kA∆T/L [121]. Therefore, for our single crystal z-cut quartz plate withA ≈ 3× 0.1 mm 5 and L ≈ 4 mm: Q˙ ≈ 10W/m.K× 3mm× 0.1mm∆T/(4mm) =7.5×10−4∆T W/K. Considering a thermal power of 0.5 W on the sample side ofquartz, ∆T between two quartz ends can be 667 K, which is more than what we4There are lots of materials with only one of these conditions which are useless. For example,sapphire and alumina have only the first condition, and metals like copper have only the second one.5Between quartz pieces with thickness of 0.5, 0.3, and 0.1 mm, thinner quartz was chosen tolower the thermal conduction between sample and sample stage.32need (∆T = 500K). As a result, there can be a safe 500 K temperature differencebetween the two sides of the quartz.Therefore, the custom heater stage was designed with a 3×6×0.1 mm singlecrystal, z-cut quartz plate serving as a thermal insulator at high temperature, whileoffering effective thermal coupling at cryogenic temperatures. The quartz platewas cut from a piece of commercially available, z-cut quartz, uncoated windowwith a diameter of 10 mm from “Meller Optics, Inc.” [125]. Samples were gluedto one end of the plate, while the opposite end was glued to the copper body ofthe stage [Figure 3.7 and Figure 3.9]. In addition to the quartz piece, a flow ofnitrogen or helium gas inside the LHe flow cryostat bath was used throughout theannealing process inside the UHV chamber to help keep other parts of sampleholder thermally connected to the room temperature environment.Annealing temperatures were achieved by driving current through the graphene,from three contacts on one edge of the sample as a source to three on the oppositeedge as a drain. In other words, we used graphene samples as their own heater. Inreality, a power between 0.5 to 1.25 W was necessary to warm the graphene sam-ples to 900 K. For example, a 50 mA current through the graphene required 25 V,giving 1.25 W dissipation and raising the sample temperature to 900 K, while otherareas in the sample holder stayed below 350 K. Elevated chip temperatures weremonitored with a 13 µm Chromel/Alumel thermocouple from “Omega Engineer-ing, Inc.” between the chip and the quartz plate 6. Such a thin thermocouple wasused to avoid making any thermal connection through the thermocouple betweenthe sample and the TC+ and TC- pins [Figure 3.7]. To make sure the temperatureof the pins and the top part in the sample holder would not warm up too much,another thermocouple was attached to them and their temperature was monitoredin two different 900 K annealing runs.3.7 Electrical connections to the samplesFor large graphene samples (with area ≥ 30µm×100µm) 7, H20 silver epoxy wasused to make an electrical connection between the graphene contacts, which are6The Cernox sensor was replaced by this thermocouple.7The size of CVD and SiC samples was large. For more details about different type of graphene,see Section 4.1.33Figure 3.9: Photograph of different samples installed on heater stage: (a)SiC2, (b) SiC3, (c) pads, the gold wires, and pins in the sample holder. However, small graphenesamples made by exfoliation are usually very sensitive to electrical shock and maybe destroyed in the process of connecting wires to their contacts by silver epoxy.For those samples, we prefer to connect their contacts to the pins by wire bondingbecause the connecting process will be done by a well-grounded (earthed) machine.To do this, a two-part sample holder was used. The bottom connector was similarto the heater stage but instead of quartz plate, a custom-made sapphire chip carrierwith separate gold pads was employed [See Figure 3.10 (a)]. The chip carrier wasmade from three pieces of sapphire. The surface of the larger bottom piece wascovered totally by gold. The two other smaller pieces were pasted on top of thelarge piece on its two sides, with silver epoxy. One smaller piece has four separategold pads and the other has three pads. While the sample was glued to the bottomgold pad to make a back gate contact, the sample pads were wire bonded to thepads of the chip carrier. Each gold pad in the chip carrier was connected to one ofthe pins in the sample stage (i.e., the bottom piece of the sample holder). Between34Figure 3.10: Photographs of (a) sapphire chip carrier, (b) wire bonded EXF2on sample stage (bottom piece of sample holder) placed on a aluminumholder, and (c) commercially available chip carrier (10.7 mm×10.7mm) with SiO2/Si chip (5 mm×5 mm) mounted. Wire-bonding padsare visible as rows on the die. Pads near graphene sample are wirebonded.the two top sapphire pieces, a Cernox temperature sensor was added, which wasshielded by a copper box. The sapphire chip carrier and the whole sample stagecan be seen in Figure ThermometersKnowing the exact temperature of graphene samples is important for weak local-ization and superconductivity measurements. It is also essential to monitor thechange in temperature of the sample throughout measurements and adatom depo-35sition. In our setup, the temperature of the cryostat’s cold finger can be monitoredwith a silicon diode (Lakeshore DT-670B-SD) installed by the factory [See Fig-ure 3.1 (b)]. To measure the temperature of the graphene sample more accurately,a CernoxTM resistance sensor (CX-1050-BG-HT) with a small copper foil shieldwas attached to the wall of sample holder with H77 epoxy to check the temperatureof sample directly [See Figure 3.1 (b)]. The Cernox was replaced with a thermo-couple for the samples which required high-temperature annealing. In additionto these thermometers, cryogenic temperatures in the graphene were monitoredvia the electron-electron contribution to resistivity and weak localization measure-ments, as will be explained in Section 7.2. The temperature measurements bydiode, Cernox, and weak localization agreed and confirmed each other. Furtherdetails about thermometery are provided in Section A.12.3.9 30 K ShieldIn addition to the magnet frame, which acts as a 4 K shield, a copper radiationshield was designed to surround everything including the magnet frame and sampleholder. This outer shield is a continuation of the 30 K gold-plated radiation shieldon the cryostat [See Figure 3.1 (b)]. A copper adapter was used to connect thesetwo shields using screws. Figure 3.11 (a) shows the gold-plated shield with adapterinstalled on it. The outer shield is a cylinder with a circular hole in the middle ofits base [See Figure 3.11 (b)]. The hole allows evaporated adatoms to reach thesample. Two additional parts were also attached to the outer shield to make apath for a shutter to open and close the hole [See Figure 3.11 (c)]. A piece ofcopper braid glued to another attached part was used to make a thermal connectionbetween the outer shield and the shutter. Section A.5 gives further details about theouter shield.3.10 Thermal Evaporator: Lithium, Indium and CopperAll of the experiments described in this thesis report the effect on graphene ofadatoms evaporated in situ, in the UHV chamber described in this chapter. Theevaporation itself was accomplished with a simple thermal evaporation source,heated by driving a current through one of various boats. The source was attached36Figure 3.11: Photographs of (a) gold plated shield and its adapter, (b) outershield with its circular hole which provides a path for evaporatedadatoms to the graphene sample, and (c) outer shield, shutter and itsadditional parts.37Figure 3.12: (a) Old evaporator setup: an evaporation source placed on thebottom flange with a copper box to limit the spreading of metal vapor.(b) A 2.75 CF tee which acts a nipple to increase the distance betweenevaporation source and sample. (c) An evaporation source inside that2.75 CF tee. Both evaporation sources in (a) and (c) are Li the bottom of the chamber, as shown in Figure 3.1 (a); for most measurementsthere was an additional 4” long 2.75 CF nipple to increase the spacing betweensource and sample [See Figure 3.12]. Three different metals’ evaporation sourceswere used for this thesis project:1. Lithium was evaporated by driving current through an alkali metal dispenser(SAES Getters) located 28 cm or 13 cm below the sample stage [See Fig-ure 3.13]. Li sources were first degassed for 30 min at 6 A, and 1-2 min in7-7.5 A, after the bakeout.2. Indium was evaporated by driving current through an alumina coated tung-sten basket made by the R.D.Mathis company (part number: RDM-WBAO-1) which contained In wire (99.999%). The In source was located about 13cm below the sample stage.3. Copper was evaporated by Joule heating of Cu shot (99.9999%) via driv-ing current (4 A and 4 V) through a custom-made alumina-coated tungsten38Figure 3.13: Photograph of an alkali metal dispenser (SAES Getters) forevaporation of Li.basket as their container. The alumina-coated tungsten basket was made bywrapping 0.25 mm diameter tungsten wire around a small alumina boat, thencovering it with UHV paste and finally curing the paste by sending currentthrough it. This alumina-coated tungsten basket was located 28 cm beneaththe sample.3.11 WiringFigure 3.5 shows the map of wiring in our setup. To avoid Johnson noise 8, coldwires (i.e., wires attached to the body of the cryostat underneath the 30 K shield)were covered by ECCOSORB CR-124 epoxy [See Figure 3.5 and Figure 3.14].ECCOSORB CR-124 is a UHV compatible epoxy for attenuation in the rangeof 1-18 GHz [See Table 3.1]. For graphene samples that did not undergo high-temperature annealing, a RC filters printed circuit board (PCB) was mounted onthe cold finger between wires coming from feedthrough and wires going to the8It can be thought of as black body radiation that can propagate down the sample wiring. Forfurther detail, see Section A.7.39Figure 3.14: Photograph of manganin wires covered by black ECCOSORBCR-124 epoxy. The wires are attached to the body of the cryostat andwill be underneath the 30 K gold-plated shield which is not installedyet in this photograph.Table 3.1: ECCOSORB CR-124 epoxy’s typical attenuation. Numbers arereported from technical bulletin of ”Emerson and Cuming MicrowaveProducts”.sample [See Figure 3.5 and Section A.8]. However, the RC filters were omittedwhen we used the heater stage, because we did not want the current to heat theRC filters instead of the graphene. Further details about wiring can be found inSection A.6.40Figure 3.15: Gluing and screwing bottom connector to the magnet frame.The 3 copper alignment rods and glued RC filters PCB can also beseen in these photographs.3.12 Assembling Permanent Parts and PlacingRemovable PartsThe previous sections described the mechanical and electrical components thatmade up our experimental chamber 9. While the permanent parts of the setupsuch as the 30 K gold-plated shield, magnet frame, and bottom connector were as-sembled just for the first time [See Figure 3.1 (b), Figure 3.15, and Section A.9 forfurther detail], the removable parts like the sample holder, cover plate, 30 K outershield and shutter can be removed and placed back. In practice, the chamber wasfrequently opened, for repairs or to change samples or evaporation sources. As aresult, it was important to ensure that the process of removal and reattachment ofmany of the components was convenient.After putting in the sample, the sample holder can be plugged into the bottomconnector, which itself is screwed to the magnet frame [See Figure 3.16 (a)]. Three9In addition to those components, Section A.13 gives detailed information about other parts ofUHV setup like pumps.41Figure 3.16: (a) The sample holder is plugged in. In this photograph, anAllen Bradley resistor is glued instead of a graphene sample [See Sec-tion A.11]. The tip of three copper alignment rods can be seen in thepicture. (b) The cover plate is mounted over the sample holder and bothare screwed to the bottom connector. (c) The outer shield is mounted.(d) Shutter and its rod for connection to wobble stick are installed.copper alignment rods help us to align the male pins of the sample holder withthe female counter pins of the bottom connector. After plugging in the sampleholder, the cover plate can be placed and screwed into the bottom connector [SeeFigure 3.1 (b)]. In fact, both the cover plate and the sample holder are connectingthermally to the bottom connector with these titanium screws [See Figure 3.16 (b)].By mounting the cover plate, the 4 K shield would be complete. Mounting the 30K outer shield, as a continuation of the 30 K gold-plated shield is the next step.The 30 K outer shield can be attached to the copper adapter and the 30 K gold-plated shield by titanium screws [See Figure 3.16 (c)]. The last step is installingshutter and the stainless steel rod which attaches the shutter to the wobble stick and42Figure 3.17: Photograph of cryostat and wobble stick on the top flange ofUHV chamber.43Figure 3.18: Residual gas analyzer scan of partial pressure versus atomicmass (Z) of different gases including H2 (Z=2), water vapor (Z=18),N2 (Z=28) and O2 (Z=32)allow us to move the shutter in vacuum while moving the wobble stick in air [SeeFigure 3.16 (d) and Figure 3.1]. After mounting these components, the 8” conflatflange can put on top of the UHV chamber [See Figure 3.17]. Further informationabout these removable parts is provided in Section A.11.3.13 Operation of Experimental SetupDeposition and transport measurements were carried out on a cryogenic stage inthe UHV chamber described in this chapter, at pressures below 5×10−10 torr aftera 3-day bakeout at 100 ◦C [Figure 3.1 (a)]. After the 3-day bakeout, the partialpressure of different gases and the chamber vacuum were monitored with a residualgas analyzer (RGA) [Figure 3.18], to make sure the chamber is in UHV condition.After the 3-day bakeout, the cryostat was cooled first by liquid nitrogen to 77K, then by liquid helium (LHe) to 4.4 K. If lower temperatures were needed, tem-44peratures down to 3 K were achieved by pumping on LHe while temperatures ofthe cold finger and graphene sample were monitored by silicon diode and Cer-nox resistor. Figure 3.19 shows the whole setup during cooldown and measure-ment. Adatoms were evaporated by driving current through a thermal evaporatorlocated underneath the sample stage on the bottom flange [Figure 3.1 (a)]. The 30K shield’s circular hole was opened using the mechanical shutter during evapora-tion. For magnetoresistance measurements, the current through the magnet (whosefield was perpendicular to the sample) was provided by a a Kepco BOP20-20Mbi-polar DC power supply. The details about resistance measurement are providedin Section A.14.45Figure 3.19: Photographs of the experimental setup during cooldown. UHVchamber, electronic rack, power supply, LHe dewar, transfer tube, anddray pump for pumping LHe can be seen in this photograph.46Chapter 4Experimental DetailsIn recent years, different techniques of monolayer graphene production have beendeveloped. Using each of these graphene samples has its advantages and disad-vantages. Exfoliated graphene samples, which are made by cleaving multi-layergraphite into single layers, are 100% monolayer and have the lowest number ofdefects, the lowest dephasing rate, and the highest electron mobility [126]. How-ever, their size are limited 1. Epitaxial graphene samples on SiC, which are grownepitaxially by depositing a layer of carbon onto the crystalline silicon carbide sub-strates, and CVD graphene samples, which are grown by chemical vapor depo-sition on copper and then transferred into other substrates, can have a millimetersize. However, they have a small percentage of bilayers 2 and more defects.The large size of SiC samples, which were not contaminated with polymer re-sists in their growth process, let us contact them with shadow mask evaporationwithout using any polymer. These pristine samples were used to investigate the re-liable interaction between alkali adatom and graphene [Chapter 5, Chapter 6, andChapter 7]. The exfoliated samples were employed to probe the effect of heavyadatoms on the dephasing rate in graphene [Chapter 8]. Finally, CVD sampleswere used for comparison with other samples [Chapter 5]. Section 4.1 describesour different graphene samples and their fabrication processes. In addition to thegraphene samples, the methods and basics of our transport measurements are ex-1The maximum area of our exfoliated samples was 50 µm×10 µm.2The percentage was less than 5 % in our case.47plained in Section Graphene SamplesThree different types of monolayer graphene were used for this thesis: exfoliatedgraphene on SiO2/Si [See Figure 4.1], CVD graphene on SiO2/Si [See Figure 4.2],and epitaxial graphene on SiC [See Figure 3.9].4.1.1 Exfoliated SamplesThe three exfoliated samples (EXF1,2,3) were deposited on 5 mm×5 mm chipscut from highly doped Si wafers with a 300±15 nm SiO2 top layer. The chip canbe seen in Figure 3.10 (b) and (c). For these samples, graphene was deposited onthe SiO2 substrate by exfoliation using scotch tape. After cleaning with the RCA1 and 2 clean [For more detail, look at Ref. [127]], the exfoliation was performedusing 3M Magic Scotch tape by placing a small piece of graphite on the tape andthen cleaving it repeatedly (7 to 10 times) by pressing the tape on itself. In theend, the cleaned Si die is placed onto the adhesive surface at locations of densegraphite coverage, then removed from the tape. Finally, residues are removed fromthe die with an acetone bath cleaning step 3. The exfoliation procedure generates arandom assortment of few-layer graphene and many-layer graphene over the entirechip, which can be identified by searching the surface using an optical bright fieldmicroscope with camera attachment.Next, electron beam lithography (EBL) was carried out in three or four stagesin order to pattern metal contacts on the chosen graphene flake. Bilayer PMMA(PMMA C4 and PMMA A2) was used as a resist. For EXF1-3, the first stagedeposited 5 nm Ni/80 nm Au wire-bonding pads and alignment marks. Nickelwas used in electrical contacts because Au does not stick well to SiO2. UsingCr or Ti instead of Ni is also common. However, Ti is difficult to evaporate inour thermal evaporator and annealing at high temperatures usually leads to highcontact resistance in Ti/Au and Cr/Au contacts. Using Ni instead of Cr and Ti cansolve this problem: the contact resistance with Ni is low (∼500 Ω.µm)[128] and3It includes placing Si chips in 60 ◦C acetone bath for 10 minutes, then in isopropyl alcohol (IPA)for 5 minutes, and finally blow drying chips with nitrogen.48Figure 4.1: Microscope images of (a) EXF2, and (b) EXF1. Yellow piecesare gold contacts. (c) Scanning Electron Microscope image of EXF1.(d) Microscope images of EXF3. (e) Microscope images of EXF-BN.The BN flake has a blue color.49it does not change with annealing. To avoid Ni magnetic effects, we placed thecontacts far (with a distance twice greater than Hall bar width, i.e. ≥50 µm) fromthe Hall bar current path. The second stage made long (∼1 mm) wires leadingfrom the wire bonding pads to the close proximity of the graphene flake. The thirdstage made a pattern of ohmic contacts to graphene in PMMA and then depositedmetal (5 nm Ni/100 nm Au) over the pattern which was made in the second andthird stages. The fourth (optional) stage of EBL was used to shape graphene withoxygen plasma etching. This stage was used to make Hall bars in EXF2,3. At theend, gold pads near the graphene sample were wire bonded to a chip carrier, as canbe seen in Figure 3.10 (b) and (c).In addition to EXF1-3, we used an already fabricated device EXF-BN, whichwas an exfoliated monolayer graphene Hall bar on boron nitride (BN)/SiO2/Si sub-strate. More details about fabrication of this device can be found in Ref. [129].EXF1, EXF2 and EXF-BN were put on commercially available chip carriers [SeeFigure 3.10 (c)] which was used before making our custom-made sample holders.However, EXF3 was placed on our custom-made sample stage for wire bonding[See Figure 3.10 and Section 3.7]. Exfoliation for EXF1 and EXF3 was done byRui Yang. Exfoliation for EXF2 was done by Anuar Yeraliyev, then contacted bythe author using EBL. The EXF-BN device was made by Matthias Studer. All fourexfoliated devices (EXF1,2,3 and EXF-BN) can be seen in Figure CVD SamplesTwo CVD samples (CVD1 and CVD2) were commercially available monolayergraphene grown by chemical vapor deposition (CVD) on copper foil. CVD1 waspurchased already-transferred[130] onto a Si/SiO2 chip, then etched by oxygenplasma into a Hall bar geometry defined by electron beam lithography (EBL) 4.CVD1 was 29.5 µm wide with longitudinal Rxx contacts (i.e. center to centerdistance between two openings) separated by 88.2 µm [See Figure 4.2 (a)]. CVD2was transferred[131] in our laboratory using procedures described in Ref. [132]by Ebrahim Sajadi, then etched by the author using oxygen plasma into a square(∼700×700 µm2) defined by EBL [See Figure 4.2 (b) and (c)]. CVD samples were4As we described in Section 4.1.1, EBL is a process that involves polymer resist.50200 µm  I G Rxx (b) (c) 50 µm  (a) Rxx C D A B Figure 4.2: Microscope images of (a) CVD1, and (b) CVD2. Yellow piecesare gold pads. Graphene has a light green color in (a) and blue color in(b). (c) Photograph of CVD2 on the silicon die.electrically contacted with Ni/Au (5nm/90nm) squares defined by EBL and liftoff.After fabrication, CVD devices were annealed in forming gas (5.72 % H2, balanceN2) at 350 ◦C for 1.5 hours to remove resist residues. Figure 4.2 shows CVD1 andCVD2 devices.4.1.3 SiC SamplesSiC1 was a 3×3 mm2 epitaxial monolayer graphene grown on a weakly-doped6H-SiC(0001) surface by our collaborators at Max Planck Institute for Solid StateResearch [107]. SiC2, SiC3, SiC4 [See Figure 3.9] and SiC5, respectively 4×4mm2, 4×4 mm2, 4×2.5 mm2 and 4×2.5 mm2, were cut from commercially avail-able epitaxial monolayer graphene grown on a semi-insulating 4H-SiC(0001) sur-face [133]. Eight contacts were deposited onto the corners and edges of each SiC51sample using shadow evaporation to avoid polymer resist contamination on thegraphene surface. Contacts on SiC1,2,4,5 were 5 nm Cr/90 nm Au; on SiC3 con-tacts were 100 nm Au. Figure 3.9 shows SiC samples.4.1.4 Annealed and Unannealed SamplesSiC3,4,5 were measured with and without high-temperature annealing, whereasSiC1,2, EXF1,2,3, EXF-BN and CVD1,2 were measured directly after bakeout,without a subsequent annealing step.4.2 Basics of Transport MeasurementsOur graphene devices were single layer graphene samples 5 on a SiO2/Si or SiCsubstrate electrically connected to leads (Au or Au/Ni or Au/Cr). In the samples ondoped Si wafers with SiO2 dielectrics, a gate voltage could be applied to the backof the substrate to control the charge carrier density (i.e., the position of the Fermilevel with respect to the band structure) [See Figure 4.3 (a)].There are two common configurations for measuring transport properties, knownas two-probe and four-probe configurations [See Figure 4.3 (b), (c) and (d)]. Four-probe measurements were performed in two different geometries: Hall bar andVan der Pauw. Graphene’s transport characteristics can be strictly isolated fromcontact effects by placing contacts far from the main path of the electrons’ conduc-tion [non-invasive contacts], as can be seen in the Hall bar geometry in Figure 4.3(c). By shaping graphene to a well-defined Hall bar, the resistivity ρ can be eas-ily calculated with the formula ρ = Rxx(W/L) where W is the width of the Hallbar and L is the center to center distance of openings for Rxx contacts [53]. Inthe Van der Pauw method, the 2D conductor (in our case, graphene) can have anarbitrary shape. The resistivity of the 2D conductors without any isolated holescan be measured by using four sufficiently small contacts A, B, C and D fixed inarbitrary places along the circumference. Resistivity is measured using the relationexp(−piRAB,CD/ρ)+exp(−piRBC,DA/ρ) = 1, where the resistance RAB,CD is the po-tential difference between contacts D and C per unit current through the contacts5Our exfoliated samples were 100 % monolayer. However, CVD and SiC samples were mostlymonolayer graphene with less than 5 % bilayer flakes.52Voltage SourceAGrapheneSi (Bottom Gate)AuAuSiO2௫௫௫௫௫௫Current SourceD CA B௫௬௫௫௫௬௫௬௫௬Current SourceLW஺஻,஼஽ ௫௫௫௫VBG (tune the chemical potential)          Figure 4.3: (a) Schematic of graphene device on a silicon oxide substrate, (b)2-probe measurement, (c) 4-probe measurement in Hall bar geometry,and (d) Van der Pauw.A and B [134]. As can be seen in Figure 4.3 (d), we can choose Rxx to be RAB,CD orRBC,DA. Therefore the constant ratio of Rxx/ρ can be determined once and by mea-suring Rxx, we can find ρ . In addition to these four contacts, some other contactsare usually placed at the circumference of the Van der Pauw device to check thehomogeneity of resistance, which is expected for continuous graphene film (i.e.,without folds, cracks, or holes). When resistance is homogeneous, different pairsof contacts with the same distance have the same Rxx and resistance measurementsin different sets of contacts produce the same ρ .The charge carrier density n and the mobility µ can be deduced by Hall mea-surements, and resistivity measurements in a weak magnetic field, through the fol-lowing relations:53Figure 4.4: Conductivity (σ ) versus applied gate (Vg) voltage for mono-layer graphene CVD1 (Inset: corresponding resistance (ρ)). Some ofgraphene’s transport properties, which would change with metal adatomdeposition, such as electron and hole mobility (µe and µh), minimumconductivity (σmin) and Dirac peak and its voltage (VDg ) have beenshown in this figure. Electrons and holes should act similarly in idealgraphene. However, both strain and charged-defect scattering in realitycould break the electron hole symmetry in a graphene monolayer [135].n=1| e | dRxydB(4.1)µ =1n | e | ρ =σn | e | (4.2)where B is magnetic field, e is electron charge, and σ = 1/ρ is conductivity [53].Hall measurements can be employed in different materials including graphene.However, the 2D structure of graphene provides another way to measure chargecarrier density and mobility in graphene. In addition to Hall measurements, charge54carrier density and mobility in graphene samples can be measured by Dirac peak6 measurement in gate voltage. The graphene/SiO2/Si stack can act as a capacitor,with the silicon oxide layer as the dielectric. The charge carrier density n may bedetermined through the formula n=Q/(eA) =Cg(Vg−VDg )/(eA) where A,Cg, Vg,and VDg are substrate area, gate capacitance, gate voltage, and the voltage of theDirac peak, respectively. While the graphene device has a dimension of tens of mi-crons, the thickness of the silicon oxide layer is around 300 nm. Consequently, itis reasonable to estimate the graphene/SiO2/Si stack as an infinite parallel plate ca-pacitor. This infinite parallel plate capacitor has a capacitance ofCg = εSiO2A/dSiO2where εSiO2 and dSiO2 are permittivity and thickness of the silicon oxide dielec-tric. Therefore, the charge carrier density has a linear relation with gate voltage:n= α(Vg−VDg ) with α = εSiO2/(edSiO2). Figure 4.4 and its inset show an exampleof mobility and Dirac peak in resistance for monolayer graphene.6The notion of Dirac peak was discussed in Section 2.1 and Figure 2.1.55Chapter 5Alkali Doping of Graphene: TheCrucial Role ofHigh-temperature AnnealingThe text of this chapter is adapted from Ref. [1], an article published in in PhysicalReview B (Rapid Communication).The promise of adatom alterations to graphene’s electronic structure has beenrealized in some experiments, whereas several others have reported a surprisingabsence of adatoms’ predicted effects. For example, adatoms have been confirmedto cause charged-impurity scattering in graphene [16–18] consistent with theoret-ical predictions [19–23]. At the same time, the theoretically predicted enhance-ment of spin-orbit interaction on graphene by heavy metal adatoms like indium[28, 29, 31, 32] has not been observed experimentally [33, 34]. The experimentalresults that will be discussed in this chapter might shed some light on this incon-sistency between theories and experiments.This chapter reports a transport investigation of what is arguably the simplestof all adatom effects on graphene: charge doping by alkali atoms (Li) depositedunder cryogenic UHV conditions. Earlier measurements of the Fermi surface areafor Li-on-graphene, using angle-resolved photoemission (ARPES), confirmed thateach Li adatom contributed approximately one electron to the graphene carrier den-sity, for both cryogenic and elevated temperature deposition conditions, though the56carrier density was observed to saturate to values differing by a factor of nearly 5 inthe two experiments [49, 99]. Transport measurements of dilute potassium and cal-cium adatoms on graphene, also deposited under cryogenic UHV conditions, ob-served charged-impurity scattering due to the adatoms; these measurements wereconsistent with a similar charge transfer ∼1e−/adatom. However, doping in theseexperiments was not explored beyond approximately 1% of full coverage [16–18].The primary outcome of our experiment is the observation that alkali doping ongraphene, after deposition under cryogenic UHV conditions, in general saturatesfar below the values reported in Refs. [99] and [49]. Different types of graphene,prepared with and without resist-based processing, saturate at a 2× 1013 e−/cm2doping level after Li deposition at 4 K. Only when an in situ annealing step to 900K has been performed, prior to the cryogenic deposition, is the full doping expectedfor monolayer alkali coverage recovered. Apparently, the UHV bake-out processand even subsequent annealing to 500 or 700 K fails to prepare a pristine graphenesurface when close adatom-graphene interactions are required. A comparison ofannealing protocols sheds light on possible explanations for this effect.Measurements of this chapter were performed on seven different graphene de-vices: five epitaxial graphene samples on SiC (SiC1-5), and 2 samples grown byCVD and transferred on to SiO2/Si chips (CVD1,2). Further details about the sam-ples were provided in Section Alkali Doping of Graphene withoutHigh-temperature AnnealingFigure 5.1 illustrates mild electron doping by Li on CVD1, clearly visible as a shiftin the Dirac peak (the zero-carrier-density resistance peak) to more negative gatevoltages [Figure 5.1 (a)]. Spatial charge inhomogeneity introduced by Li adatomsbroadened the Dirac peak with each deposition. For fixed Li source current, theshift in the Dirac peak was linear in deposition time [Figure 5.1 (b)], confirmingthe constant deposition rate from the getter source over multiple depositions spreadover the ten hours required to accumulate a set of data such as that in Figure 5.1.Dirac peak shift in gate voltage is a useful probe of charge carrier density formild doping, but is ineffective at higher densities when the Dirac peak moves out5710050ΔVD(V)2015105Deposition Time (s)-6-4-20246n H(x1012cm-2)-80 -40 0 40Vg (V)12010080604020Rxx(kΩ)-100 -50 0 50 100Vg (V)dep. time0 s5 s10 s15 s20 s220210200190180170160Rxy(Ω)-100 -50 0 50 100B (mT)(a) (b)(c) (d)5 s Li dep.Vg=-60 VFigure 5.1: Li deposition at 3 K on CVD1 [2nd run]: (a) Dirac peak shiftwith consecutive Li depositions. Retraced data show repeated scans,confirming no shift of Dirac peak with time after the shutter was closed.Legend indicates total deposition time. (b) Gate voltage shift of Diracpeak center (∆VD) was linear in deposition time. (c) Example of Halldata. (d) Carrier density, nH , extracted via Hall effect at different gatevoltages for each deposition time (marker size indicates error bars).Diagonal lines [legend as in (a)] correspond to backgate capacitanceα=nH /Vg=5.0×1014 m−2V−1 with zero-crossing (vertical lines) set byDirac point at each deposition time.of the range of accessible gate voltages, and on the (un-gateable) SiC samples.Induced charge density was also monitored using the Hall effect away from theDirac point [Figure 5.1 (c)]. Hall and Dirac point measurements were consistentthroughout the accessible gate voltage range, assuming a backgate-to-graphene ca-pacitance α=nH /Vg=(5.0±0.2)×1014 m−2V−1 [Figure 5.1 (d)]. The Dirac pointmeasurements in CVD samples was used to confirm the reliability of Hall mea-surements as method for measuring charge carrier density. It is worth noting that582.∆n (x1013e-/cm2 )3002001000Deposition Time (s)CVD1CVD2, dep time×0.22SiC1SiC2SiC3Figure 5.2: Saturated doping in five samples. Source current was 7.3 A or 7.5A, except for SiC1 for which it was 7 A. Deposition times reported forCVD2 are multiplied by a geometrical factor (13 cm/28 cm)2 to accountfor different source-sample distance (see text). ninit for each depositionwas, respectively, 0.4, 0.16, 1.9, 1.7, 1.0×1013 e−/cm2 for CVD1,2,SiC1,2,3.Li vapor during evaporation was detected by a residual gas analyser positionedoff-axis. The presence of Li on the graphene surface was later confirmed by time-of-flight secondary ion mass spectrometry.Although the induced carrier density can be determined as in Figure 5.1, thedensity of adatoms on the surface could not be directly measured. The ratio be-tween the two is η , the net charge transferred per adatom. A rather wide rangeη = 0.4−1 has been predicted by DFT calculations for graphene or graphite, as-suming the Li sits on the Hollow site (at the center of a ring of carbon atoms)[3, 4, 41, 136–141]. While the experimental values of η=0.66 [99] and η = 0.5[100] extracted by ARPES from the Fermi surface area for a√3×√3R30◦ arrange-ment of Li on graphene, an x-ray photoelectron spectroscopy (XPS) study of Li/-graphite for an Li coverage estimated between 1 and 3 monolayers found η ≈ 1[142].For higher adatom coverages on CVD1 than what is shown in Figure 5.1, thecharge carrier density saturated at 2.5× 1013 e−/cm2 [Figure 5.2], an increaseof ∆nsat = 2.1× 1013 e−/cm2 above the initial density ninit = 0.4× 1013 h+/cm2recorded after UHV bakeout but before Li exposure. Nearly identical saturateddoping levels, ∆nsat = 2× 1013 e−/cm2, were observed for CVD2, and SiC1,2,3.59In contrast, an order of magnitude larger ∆n(√3×√3)R30◦ = 2.2× 1014 e−/cm2 isexpected for the (√3×√3)R30◦ arrangement of Li on graphene at the average pre-dicted η = 0.7. It is unlikely that the anomalously low doping observed here resultsfrom processing, given that CVD1 and 2 followed different processing protocols,and SiC1,2,3 were never exposed to polymer resists. Also, the saturated dopingwas apparently not affected by initial carrier density [Figure 5.2].The saturated doping also did not depend on the current passed through thegetter, or the getter-to-sample distance. The graphene-getter distance was 13 cmfor CVD2, but 28 cm for CVD1 and SiC1,2,3. If radiative heating from the sourceallowed adatoms to move around, for example to dimerize, this effect should havebeen stronger for CVD2 compared to CVD1. After scaling deposition time bythe geometrical factor (13 cm/28 cm)2 to account for different source-sample dis-tances, even the rate of doping increase was the same [Figure 5.2] for CVD1 andCVD2. The results of each deposition in Figure 5.2 were reproduced in a secondrun with the same getter source, confirming that the saturation was not associatedwith empty Li sources.5.2 Alkali Doping of Graphene after PerformingHigh-temperature AnnealingThe one additional step that did increase ∆nsat was a post-bakeout anneal, priorto cryogenic Li deposition. Figure 5.3 illustrates the progressively higher ∆nsatfound for pre-deposition annealing temperatures 500 K and above. In all caseswhere identical preparations were performed on multiple samples, the same valuesof ∆nsat were found, validating the comparison of different SiC samples on a singlegraph. SiC3 data shows the ∆nsat = 2× 1013 e−/cm2 baseline before annealing,consistent with Fig. 4, then the order of magnitude larger ∆nsat = 2×1014 e−/cm2that was reached reached when the sample was annealed to 900 K prior to the Licryogenic deposition. SiC4 data shows that a 500 K anneal yields ∆nsat = 4×1013e−/cm2, while 700 K yields ∆nsat = 9×1013 e−/cm2, and that ∆nsat is independentof annealing time. We note that the value ∆nsat = 2× 1014 e−/cm2, recorded inSiC3 after a 900 K anneal, is considerably larger than the ∆nsat ∼ 9×1013 e−/cm2found in Ref. [49] for cryogenic deposition under nearly identical conditions.6020151050∆n (x1013e-/cm2 )160012008004000Deposition Time (s)SiC3: before annealingninit=1.0×1013e-/cm2SiC3: 1 hr 900 K annealninit=2.3×1013e-/cm2SiC4: 1.5 hr 500 K annealninit=2.2×1013e-/cm2SiC4: 1.5 hr 700 K annealninit=2.2×1013e-/cm2SiC4: 6 hr 700 K annealninit=2.9×1013e-/cm2SiC5: 2.5 hr 900 K anneal& exposure to airninit=2.4×1013e-/cm2Figure 5.3: Change of carrier density ∆n versus Li deposition time forSiC3,4,5, before and after annealing. The Li evaporation source wasnot changed between subsequent measurements of a given sample; get-ter current was 7.5 A in all cases.The effect of Li adatoms on sample mobility is also drastically reduced beforecompared to after annealing, consistent with the doping effects described above.Before annealing, the mobility of SiC3 decreased by less than a factor of 2 due toLi, from 1475 cm2/Vs to 898 cm2/Vs. But after annealing at 900 K, the mobilitydecreased by over a factor of 20, from 712 cm2/Vs to 37 cm2/Vs for SiC3. A moredetailed investigation of the effects of Li adatoms on scattering in graphene will bedescribed in the next chapter.How can we understand the saturation of doping at 10% of the expected levelfor unprocessed epitaxial graphene after a standard UHV bakeout? Conversely,what changes are induced on the surface by the 500, 700, and 900 K anneals,that raise the saturated doping levels by an order of magnitude? In order to ad-dress these questions, SiC5 was first annealed at 900 K, then exposed to air for 2.5hours, then baked out a second time before Li deposition. Air exposure would pre-sumably not alter surface reconstructions due to the anneal, but difficult-to-removeatmospheric contaminants such as H2O might return.As can be seen in Figure 5.3, the intermediate air exposure reduced ∆nsat backto 3× 1013 e−/cm2, not far above the unannealed value. This result suggests that61limits on ∆nsat are primarily due to atmospheric gases absorbed on the graphene,rather than defects that are healed by high temperature annealing in UHV [143–147]. However, the increase in ∆nsat from 700 to 900 K annealing temperatureindicates these adsorbates are not fully removed even by anneals up to 700 K.This observation is difficult to reconcile with data from several groups indicatingdesorption temperatures for H2O on graphene from 150 K to 400 K [148–150]. It iswell established that H2O, O2, H2, and N2 intercalate between monolayer grapheneand its substrate (in many cases SiC) [149, 151–161]. On the other hand, it is notstraightforward to identify a mechanism by which these intercalants would affectthe doping efficiency of surface Li adatoms.Although the data above have focused on ∆n, annealing also affected the pre-deposition carrier density ninit. Annealing above 500 K increased the carrier densityin bare SiC samples from 1−1.7×1013 e−/cm2 to 2−2.7×1013 e−/cm2, thoughexact values varied sample to sample. After a first Li deposition step, annealing at500 K brought ninit close to its pre-Li value. However, some indications were foundthat the desorption process for Li even after a 900 K anneal was not complete; thisdesorption will be the topic of a future study.The data reported here motivate a more careful examination of the graphene-vacuum interface under UHV conditions, and how it evolves during annealing, viasurface-sensitive techniques such as STM or LEED. At the same time, they demon-strate that reliable adatom-graphene interactions can be achieved only after in situhigh temperature cleaning procedures. This observation may explain the difficultymany groups have faced in inducing superconductivity, spin-orbit interaction, orsimilar electronic modifications to graphene by adatom deposition, and points to-ward a straightforward, if experimentally challenging, solution.It is worthwhile to add that the 700 K/900 K annealing process which wasperformed on SiC samples might be problematic for graphene on SiO2 substrate.Annealing at 700 K makes graphene conform closer to SiO2 substrates and maylead to degradation of graphene devices electrical performance, such as broadeningof the Dirac peak and shifting it to positive voltages due to hole doping from thesubstrate [162]. On the other hand, SiC samples are not ideal for some experimentslike enhancement of spin-orbit interaction by adatom due to their higher dephasingrate compared to exfoliated graphene on SiO2. One potential solution for annealing62exfoliated samples without degrading them is using boron nitride as the graphenesubstrate.63Chapter 6Alkali Induced Short-rangeScattering: Intervalley Scatteringin Li-doped GrapheneThis chapter investigates the effects of Li adatoms on scattering and magnetocon-ductance in monolayer epitaxial graphene on SiC, in continuation of Chapter 5which showed the crucial role of 700 K/ 900 K annealing prior to Li deposition[1]. High-temperature annealing, Li deposition, and measurement of magneticfield dependence of the sample resistivity were all performed in situ, under cryo-genic ultrahigh-vacuum (UHV) conditions. The major finding of this chapter is asignificant decrease of the intervalley time τi and intervalley length Li by Li depo-sition for the samples that were annealed to 700 K and 900 K prior to cryogenic Lideposition. As we will show, this enhancement of intervalley scattering means Licaused short-range scattering in the sample. This is the first experimental evidenceof short-range scattering due to alkali adatoms in graphene, a result that contra-dicts the naive expectation that alkali adatoms on graphene only cause long-rangeCoulomb scattering [See Section 2.4].Measurements of this chapter were performed on four epitaxial graphene sam-ples on SiC (SiC1-4). Further details about the samples were provided in Sec-tion 4.1.3. As we described in Chapter 5, graphene samples SiC4 and SiC3 wereannealed in UHV at 700 K and 900 K, respectively. Then Li was deposited on640.∆σ(e2 /h)-100 -50 0 50 100B (mT)∆n=0∆n=9.3×1013e-/cm2Figure 6.1: Effect of Li deposition on T=3 K magnetoconductivity of theSiC4 which was annealed to 700 K prior to cryogenic deposition. Thesolid lines are fits to Equation 2.6. The charge carrier densities n fromthe top curve to the bottom one are 2.18, 5.54, 7.45, 10.14, 11.48×1013e−/cm2. The change of charge carrier densities ∆n are shown in thegraph.SiC3,4 at cryogenic temperature 1. While Li doping on these sample was studiedin the last chapter, we will use the weak localization correction to magnetoresis-tance to probe intervalley scattering in this chapter.6.1 Weak Localization in Li-doped GrapheneFigure 6.1 shows the effect of varying lithium coverages on graphene’s low fieldmagnetoconductivity. The top trace corresponds to the graphene sample before Lideposition, while for the lower traces, the sample is decorated with Li adatoms. Aswe discussed in Section 2.2, dephasing time τϕ , intervalley time τi, and intravalleytime τ∗ can be extracted by fitting magnetoconductivity curves to Equation 2.6.The characteristic fields Bϕ,i,∗ in Equation 2.6 are related to the times by τϕ,i,∗ =h¯/(4eDBϕ,i,∗) where D is the diffusion constant. Furthermore, their relation withcorresponding lengths can be written as L2ϕ,i,∗ = h¯/(4eBϕ,i,∗).Intravalley scattering is very fast in our epitaxial graphene on SiC, correspond-ing to a very short time τ∗ and a large characteristic field B∗ that suppresses thesecond term in Equation 2.6. This is a common phenomenon in graphene samples1Li was also deposited on SiC1,2 at cryogenic temperature. However, no high-temperature an-nealing was performed on them prior to the cryogenic deposition.652.τ φ(x10-12s-1 )1086420∆n (x1013 e-/cm2)∆σ(e2 /h)-10 -5 0 5 101/τΒ(x1015 s-1)(a)(b)Figure 6.2: (a) The magnetoconductivity curves of Figure 6.1 versus τ−1B =(4eD/h¯)B. The curves are shifted in y for clarity. (b) Fitted dephasingtime versus change of charge carrier density induced by Li depositionfor SiC4 after annealing.[57] especially in high densities due to the influence of trigonal warping [163].There are two remaining scattering times, τϕ and τi, to fit 2. Let us first look at thedephasing time, τϕ .Since the extraction of these scattering times depends on diffusion constantD, it is more useful to compare the magnetoconductivity curves plotted versusτ−1B = (4eD/h¯)B to take into account changes of the diffusion constant [Figure 6.2(a)]. As can be seen in Figure 6.2 (a) and (b), the similar curvature of magneto-conductivity in the narrow range of τ−1B shows that dephasing time did not have ameaningful change as charge carrier density varied due to Li deposition. This isnot surprising because Li, as a light adatom, is not a source of spin-orbit couplingor magnetism. On the other hand, an unexpected and interesting phenomena was2Numerical estimates of τϕ = L2ϕ/D= h¯/(4eDBϕ ) and τi = L2i /D= h¯/(4eDBi) can be obtainedby fitting our data to Equation 2.6.66observed in intervalley scattering, which will be discussed in the next section.6.2 Effect of Li Deposition on Intervalley Scattering inGrapheneFigure 6.2 (a) shows that the shape of the WL curve changed significantly, whenconsidering a wide range of τ−1B . The width of the WL curve is directly related tothe strength of intervalley scattering [164], and fits of Equation 2.6 to the WL dataindicate a sharp decrease in τi and Li due to Li deposition [See Figure 6.3]. Thisindicates that intervalley scattering was significantly enhanced by Li deposition forSiC3,4.As can be seen in Figure 6.3, the fitted values of τi and Li after Li deposition arerepresented by a range rather than a single datapoint with error bars because, afterthe first Li deposition, τi and Li were already so low that they could not be reliablydistinguished from zero. In order to estimate possible ranges for the extractedvalues τi and Li, we tried to fit the magnetoconductivity graph with different Biand observed the normalized chi-square value χ2v 3. In the lowest fitted Bi (i.e.,the upper limit of the fitted τi and Li), the normalized chi-square value starts toshoot up (χ2v ≈2) [Figure 6.4 shows an example] and fit clearly deviates from themeasured graph. Due to the limited range of the magnetic field, no upper limit forBi could be determined (i.e., the lower limit of the fitted τi and Li is 0.).The decrease of both τi and Li shows that the effect of Li deposition on in-tervalley scattering is not a result of change solely in diffusion constant D. Howthen should we understand the enhancement of intervalley scattering after Li de-position? As we discussed in Section 2.4, there are two main mechanisms forscattering in graphene: long-range (LR) Coulomb interactions for charged impuri-ties [16, 18, 19, 21, 22, 62] and short-range (SR) interactions due to atomic-scaledefects [63] and covalent bonding of adatoms with graphene [34, 66, 67].Now, let us see if the LR Coulomb potential of charged impurities, which is3The chi-square may be defined as Σ((y− yi)/wi)2 where y is a fitted value, yi is the measureddata value and wi is the standard error for the given point. The normalized chi-square, which is alsocalled the reduced chi-square, is defined as the chi-square per degree of freedom (i.e., number ofmeasurements minus number of fitting parameters). While a value of χ2v =1 indicates that the extentof the match between measurement and fit is in accord with the error, a χ2v 1 indicates a poor fit[165].671.τ i(x10-12s)LR theory (d=1.63 Å,SR+LR theory (Ueff=1.28 eV, τi(∆n=0))(a)300250200150100500L i(nm)20151050∆n (x1013 e-/cm2)LR theory (d=1.63 Å)LR theory (d=1.63 Å, Li(∆n=0))SR+LR theory (Ueff=1.28 eV)SR+LR theory(Ueff=1.28 eV, Li(∆n=0))(b)LR theory (d=1.63 Å)τi(∆n=0))SR+LR theory (Ueff=1.28 eV)Figure 6.3: (a) and (b) Fitted intervalley time and length versus change ofcharge carrier density induced by Li deposition for SiC3 (red) and SiC4(blue). While the brown line shows the theoretically predicted interval-ley time/length from long-range (LR) scattering considering d=1.63 A˚,the green line shows the theoretically predicted intervalley time/lengthfrom both short-range (SR) and long-range (LR) scattering consideringSR potential amplitude Ue f f = 1.28eV . The broken lines are the samecalculations plus incorporating the initial intervalley scattering that ex-isted in graphene before Li deposition.expected for alkali adatoms on graphene [3, 40, 42–44], can explain enhancing in-tervalley scattering by Li deposition. To avoid considering D in our calculations,we focus on change of τi , instead of Li, versus impurity density nimp using Equa-tion 2.15 [See Section 2.5]. It is reasonable to assume nimp = ∆n/η where ∆n ischange of charge carrier density due to adatom deposition and η is the net chargetransferred per adatom. We use η = 0.9, which is the theoretically predicted valuefor Li charge transfer as Refs. [3], [139], and [137] reported 4.4As discussed in Chapter 5, a rather wide range η = 0.4−1 has been predicted by different DFTcalculations for graphene and graphite, assuming the Li sits on the hollow site (at the center of a ringof carbon atoms) [3, 4, 41, 136–141]. Also a range η = 0.5− 1 has been reported experimentally682015105Normalized chi-square value120100806040200Li (nm)SiC4 700 K; ∆n=3.36×1013 e-/cm221Figure 6.4: The normalized chi-square value versus different possible Li forthe second point in Figure 6.3.As can be seen in Equation 2.15, LR-induced τi depends exponentially on d,the impurity distance from the graphene plane [For more details, see Section 2.5and Ref. [72]]. Plugging our measured values for τi and nimp of SiC4 that wasannealed to 700 K 5 into Equation 2.15, we find that the Li atoms would have to bea distance of less than 1 A˚ from the graphene plane in order for the intervalley rateto be explained by LR scattering. This is much smaller than the theoretically pre-dicted d which is in the range of 1.63-2.1 A˚ for Li adatoms on hollow sites above thegraphene hexagon [41, 76, 136, 137, 139, 141, 166, 167]. In other words, even ifwe use the smallest predicted value d=1.63 A˚ for calculating τi from LR scattering,the charged impurity scattering cannot explain the observed decline in the interval-ley time. The brown lines in Figure 6.3 (a) show the calculation from long-rangescattering, and clearly do not fit the data. In order to be more accurate, we also in-corporate the initial intervalley scattering rate τ−1i,0 in graphene before Li depositionto this theoretically predicted scattering τ−1i,LR and plot the resulting τi with a broken[99, 100, 142]. However, as we will show in Section 6.3, the value of η = 0.9 is extracted from ourmobility data.5For the (√3×√3)R30◦ arrangement of the Li monolayer on graphene in the range η = 0.5− 1,∆n(√3×√3)R30◦ = 1.6−3.2×1014 e−/cm2 is expected. While the values of ∆n for SiC3 annealed to900 K are close to or more than one Li layer, the maximum value of ∆n for SiC4 annealed to 700 Kis around or less than half the value for the Li monolayer. Therefore, it is reasonable to assume thateach Li adatom in SiC4 annealed to 700 K still acts like a single scattering center.69brown line in Figure 6.3 (a): τ−1i = τ−1i,0 + τ−1i,LR =⇒ τi = τi,0τi,LR/(τi,0+ τi,LR) 6.Another possibility which might come to the mind is that high charge car-rier density or LR scattering by Li could somehow enhance any pre-existing SRscattering in the graphene, for example due to lattice defects. While it is shownexperimentally that intervalley length in normal graphene does not depend on gatevoltage (i.e. charge carrier density n) [163, 168, 169], the intervalley scatteringin defected graphene was shown to be suppressed by applying negative gate volt-age or depositing calcium adatoms, due to changing the initially neutral defects tocharged defects [164]. As Ref. [164] showed, adding a source of LR potential toa sample already having strong SR scattering can reduce the transport cross sec-tion of the SR scattering, and as a result will suppress intervalley scattering. Thischange is the reverse of what we observed and cannot explain the enhancement ofintervalley scattering.Instead, one might consider intervalley scattering due to electron-phonon in-teraction as a possible explanation, especially due to the fact that Li deposition isbelieved to enhance the electron-phonon coupling in graphene [24, 49, 99]. How-ever, a careful look at the theory of intervalley scattering due to electron-phononinteraction rejects this idea. Naturally, the zone-boundary phonons (i.e. phononsaround the K and K’ points) which are high energy phonons of short wavelength,comparable to the lattice constant, can give an electron the momentum necessaryfor the transition between the K and K’ points [81]. Therefore, the intervalleyrate of electrons of excess energy E (i.e. electron’s total energy minus Fermienergy) due to emission of zone-boundary phonons of the frequency ωK can befound through 1/τi = (piλK/h¯)(E− h¯ωK)Θ(E− h¯ωK) where λK is a dimensionlesselectron-phonon coupling constant and Θ is the Heaviside function [81, 83, 170].Consequently, the phonon emission is possible only when the initial electron en-ergy is larger than the phonon energy to be emitted [81]. Unlike ARPES or otherkinds of spectroscopy in which photons give electrons excess energy to create in-tervalley scattering due to electron-phonon coupling [82, 171], the only source ofelectron energy in our transport experiment is temperature. The zone-boundary6Similar lines can be seen in Figure 6.3 (b) for Li. The broken line in that picture is coming fromthe following formula: L−2i = L−2i,0 +L−2i,LR =⇒ Li = Li,0Li,LR/√L2i,0 +L2i,LR70phonon energy is at least 124 meV [81–83] which is much larger than kBT evenat room temperature with kBT =25 meV. Therefore, electron-phonon interaction isirrelevant to the intervalley scattering in our samples.With long-range (LR) and electron-phonon scattering unable to explain the ob-served enhancement of intervalley scattering, we turn to short-range (SR) scatter-ing as a possible explanation. As discussed in Section 2.4, SR scattering centersimpose a potential of the form U =Ue f fΣNn=1δ (Rn− r) where Ue f f , N and Rn areSR scattering potential amplitude, the number and location of scattering centers,respectively [51]. Considering impurities that produce both LR Coulomb potentialand a delta function SR potential, Ref. [75] shows that the intervalley scatter-ing rate is given by Equation 2.17. Using the dielectric constant of our substrate(kSiC = 13.52), Equation 2.17 would be 1/τi[s−1] = 1.775× 10−2nimpU2e f f ε0.537Fwith nimp in units of cm−2 and Ue f f and εF in unit of eV. Plugging measured datain this formula, we find that Ue f f ≥ 1.28 eV would explain our observations. InFigure 6.3, the green lines show the calculated intervalley time and length from SRscattering theory with Ue f f = 1.28 eV and broken green lines are the same calcu-lations after incorporating the effect of the initial intervalley scattering in pristinegraphene.6.3 Effect of Li Deposition on Mobility and DiffusionConstant in GrapheneSeveral reports in the literature have used transport measurements of dilute potas-sium and calcium adatoms on graphene, also deposited under cryogenic UHV con-ditions, to quantify charged impurity (LR) scattering by studying the change ofinverse mobility versus impurity density [16, 18, 39]. In this section, we perform asimilar analysis on data from our measurements.Charged impurity scattering in graphene results in a simple relation betweenmobility µ and impurity density nimp as µnimp = C where C is a constant thatdepends on the dielectric constant of the substrate [See Equation 2.8 and Equa-tion 2.9 in Section 2.4]. For 4H-SiC which is the substrate of our annealed samples(SiC3,4) with kSiC = 13.52, C = 36.75e/h ≈ 9× 1015 V−1.s−1 [See the discus-sion after Equation 2.9 in Section 2.4]. Assuming nimp = ∆n/η , we would have715004003002001000D (cm2 /s)20151050∆n (x1013 e-/cm2)SiC4 500 KSiC4 700 KSiC3 900 KLR Theory(b)(a) 3002502001501005001/µ(V s/m2 )SiC4 700 K LR fit (η=0.9)SiC3 900 K LR fit (η=0.9)LR+SR fit (Ueff=1.28 eV, η=1)LR+SR fit (Ueff=1.28 eV, η=0.9)Figure 6.5: (a) The inverse mobility versus change of charge carrier density∆n induced by Li deposition for the SiC3 and SiC4 samples which wereannealed to 700 K and 900 K prior to cryogenic Li deposition. Whilethe solid lines are the LR fits, the broken lines are LR+SR fit consid-ering Ue f f=1.28 eV. (b) Measured diffusion constant D of annealedSiC3,4 versus change of carrier density induced by Li which is con-sistent with the values coming from long-range (LR) charged scatteringtheory [shown with brown line].1/µ = ∆n/(ηC).Consistent with LR scattering, 1/µ of annealed samples (SiC3,4), has an ap-proximately linear relation with ∆n and therefore with nimp [Figure 6.5 (a)]. UsingC= 9×1015 V−1.s−1 and the slope in the graph in Figure 6.5 (a), we find η = 0.9,consistent with the theoretically predicted value for Li charge transfer as Refs. [3],[139], and [137] reported 7. It is noteworthy to mention that the formula for thediffusion constant due to Coulomb LR scattering [Equation 2.10] is also consistent7There is a possibility that a range η = 0.6− 1 could be considered consistent with our data.Using the values in the range η = 0.6−1 givesC = 1−0.8×1016 V−1.s−1 which still has the sameorder of magnitude as the predicted value of C ≈ 9× 1015 V−1.s−1. If SiC has a higher dielectricconstant or some of Li adatoms make dimers or trimers, the real η can be less than 0.9, even withconsidering the exact theoretically predicted C ≈ 9×1015 V−1.s−1.72with our measured values as can be seen in Figure 6.5 (b).Given that the observed mobility change is consistent with LR scattering, butthe previous section indicated that SR scattering was also involved, what hap-pens to the analysis if both mechanisms are taken into account? According toMatthiessen’s rule, the total mobility in this case can be written as 1/µ = 1/µLR+1/µSR. While LR mobility µLR can be calculated as we described before (1/µLR =∆n/(ηC)), SR mobility µSR may be calculated through 1/µSR=BU2e f f (∆n+n0)(∆n/η)[See Equation 2.13], where B is a constant and n0 is the charge carrier density ofpristine graphene. As can be seen in Figure 6.5 (a), this LR+SR fit works evenbetter than the LR fit on our data. The LR+SR fit for mobility also can be used todetermine an upper limit on Ue f f . Ue f f ≥ 2.5 would imply η >1, which is unrea-sonable for Li. Therefore, we can estimate a range for the SR scattering potentialamplitude Ue f f for Li adatoms: between 1.28 to 2.5 eV 8.When there are both LR and SR scattering, SR scattering can be challengingto detect in 1/µ data especially when the impurity concentration is small. Since1/µSR ∝ n2imp, 1/µSR just makes a small percentage of 1/µ in low nimp regime9. Therefore, it is not surprising that experiments of Ref. [16], [17], and [18]with dilute concentrations (≤ 1% of full coverage) of K and Ca did not explore SRscattering. Even in our case of high nimp regime withUe f f = 1.28 eV, 1/µSR makesonly less than 10 % of 1/µ . As a result, linear LR fit is still working in our case.As discussed in Section 2.4, the SR scattering potential amplitude Ue f f for anadatom on graphene may be estimated through the following formula [51, 61]:Ue f f =t2ad−gr| EF −Ead |(6.1)where EF is the Fermi energy in graphene, Ead is the on-site energy of the electronin the unperturbed adatom, and tad−gr is the hopping amplitude between adatomand carbon atoms in graphene. For comparison, we can obtain an estimate forUe f ffrom Equation 6.1. Ref. [76] gives a value of 0.58 eV for the | EF −ELi |. To the8Note that all of presented mobility data in this section were taken from samples SiC3,4 whichwere annealed prior to cryogenic Li deposition. To look at data from unannealed samples, please seeAppendix B.9It is worth noting that correlations in impurity positions will also produce µ supralinear in nimp[17]. However, it can be ruled out in our case due to the observed changes in τi.73best of the author’s knowledge, there is no calculation of tLi−gr in the literature.However, there is a theoretical study of potassium on graphene with the suggestedcalculated value of tK−gr = 1 eV [172]. Using this value with the measured energyoffset gives Ue f f ≈ 1.7 eV for Li, consistent with our data.6.4 ConclusionTransport properties and magnetoconductance of four different epitaxial mono-layer graphene samples decorated with lithium adatoms were measured in a custom-built UHV cryostat, at electronic temperatures of 3 K and above. High-temperature(700/900 K) annealing of graphene prior to cryogenic Li deposition, not only en-hances the doping effect, it also enhances Li adatoms’ effect on intervalley scat-tering. Enhancement of intervalley scattering is a sign of short-range scattering.Our report is the first experimental evidence for the short-range scattering of alkaliadatoms on graphene and its effect on enhancing the valley relaxation. Change ofmobility due to Li deposition also confirms that Li adatoms cause both of long-range and short-range scattering in graphene. A range of 1.28 eV ≤ Ue f f < 2.5eV was estimated from our data for short-range scattering potential amplitude ofLi adatoms on graphene.74Chapter 7Li Induced Superconductivity?In addition to doping and charged impurity scattering, alkali adatoms in generaland lithium in particular are expected to increase electron-phonon coupling in thegraphene to the point that superconducting critical temperatures of several Kelvinor more are achieved [24, 25, 48, 84]. Superconductivity has been reported in few-layer graphenes and graphene laminates doped with Li, Ca, or K via intercalation[93–98]. The only report of superconductivity in alkaline decorated monolayergraphene in the literature came recently from an angle-resolved photoemission(ARPES) measurement of epitaxial SiC graphene, onto which Li adatoms weredeposited by physical vapor deposition at cryogenic temperatures [49]. We lookedfor possible signatures of superconductivity in the resistivity of Li-doped graphene,emulating as closely as possible the conditions in Ref. [49]. But no suppression ofresistivity consistent with incipient superconductivity was observed down to 3 K,compared to Tc = 5.9 K inferred from the gap seen in the ARPES data in Ref. [49].7.1 No Signatures of Superconductivity above 3 KAfter each Li cryogenic deposition, the samples were allowed to cool down totheir base temperatures (3 K for SiC1,2,3 or 4 K for SiC4) 1 and their resistanceand magnetoresistance were recorded. While change of charge carrier density ofSiC3 that was annealed to 900 K prior to cryogenic deposition saturated at the full1The sample temperature rose by at most 1 K during evaporation.75394392390388386Rxx(Ω)SiC4 700 K∆σ=0.73(e2/h)(c)422420418416414Rxx(Ω)SiC3 900 K∆σ=0.64(e2/h)(a)181.2180.8180.4180.0Rxx(Ω)987654T (K)SiC3∆σ=0.67(e2/h)(b)122.6122.4122.2122.0121.8Rxx(Ω)864T (K)SiC4 500 K∆σ=1.08(e2/h)(d)Figure 7.1: Longitudinal resistance Rxx versus temperature T after saturationof Li deposition for SiC3 (a,b), and SiC4 (c,d) with and without 700/900K annealing prior to cryogenic Li deposition. Values of ∆σ shown ineach panel indicate the equivalent change in conductivity (after includ-ing geometrical factors) from the lowest temperature to 9 K.coverage, saturation for other samples that were annealed at lower temperature ornot annealed occurred sooner [See Chapter 5]. Using the linear-in-time increasein carrier density for low doping, we estimated the deposition time required forcomplete√3×√3R30◦ coverage that has been used in calculations of superconduc-tivity enhancement, and made sure to investigate depositions up to and beyond thetime required for complete coverage. After the last Li deposition for each sample,we let the sample warm up [Fig. 7.1]. In no case, was a sharp drop in resistivityobserved down to 3 or 4 K. Instead, the temperature dependence of the resistancewas weakly insulating [Fig. 7.1], consistent with conventional weak localizationand electron-electron interaction effects.We looked for superconductivity in samples that were annealed at high-temperature[e.g., Fig. 7.1 (a) and (c)] as well as samples without high-temperature anneal-ing [e.g., Fig. 7.1 (b) and (c)]. While high-temperature (700/900 K) annealing ofgraphene prior to cryogenic Li deposition enhanced the saturation to a level equalto or more than saturation density in Ref. [49], still no sign of superconductivity760.∆σ(e2 /h)1000-100B (mT)(b)280260240220200τ φ−1(x109s-1 )76543T (K)(c)∆σ(e2 /h)-10 -5 0 5 10B (mT)2.7 K4.4 K7.0 K(a)137.3137.2137.1137.0136.9136.8σ-σWL(e2 /h)2 3 4 5 6 7 8 9T (K)(d)Figure 7.2: (a,b) Narrow and broad magnetic field ranges for the magne-toconductivity of the pristine SiC1 graphene device, showing fits toEquation 2.6. (c) Extracted dephasing rate τ−1ϕ (T ) with linear fit. (d)Graphene conductivity after subtracting the contribution due to weaklocalization, with linear-log fit.was observed.One might think that the absence of superconductivity in transport might becaused due to an electronic temperature well above the cryostat temperature. How-ever, our analysis of electronic temperature in the next section argues against thisidea.7.2 Electronic TemperatureTo confirm that the absence of superconductivity in transport cannot be attributedto an electronic temperature well above the cryostat temperature, we analyzed theeffects of weak localization and electron-electron interactions for pristine graphenesamples placed on the sample holder with and without the heater stage. WhileFigure 7.2 shows the data for SiC1 on a normal sample holder without a heaterstage, Figure 7.3 and Figure 7.4 show the data for SiC4 on the heater stage after770.∆σ(e2 /h)1050-5-10B (mT)2.9 K4.3 K6.0 K(a)∆σ(e2 /h)-100 0 100B (mT)(b)440420400380360340τ φ−1(x109s-1 )6543T (K)(c)163.5163.0162.5162.0σ-σWL(e2 /h)2 3 4 5 6 7 8 9T (K)(d)Figure 7.3: (a,b) Narrow and broad magnetic field ranges for the magneto-conductivity of the pristine SiC4 graphene device annealed to 500 Kprior to cooldown, showing fits to Equation 2.6. (c) Extracted dephasingrate τ−1ϕ (T ), with linear fit. (d) Graphene conductivity after subtractingthe contribution due to weak localization, with linear-log fit.two different annealing conditions.Dephasing, intervalley and intravalley scattering rates were extracted by fit-ting magnetoconductivity curves of SiC1 and SiC4 to Equation 2.6 which was ex-plained in Section 2.2. Valley scattering rates are not expected to change with tem-perature, within the range 3-7 K represented by the data. [163, 168, 169] Therefore,sets of curves for a given sample at different temperatures [e.g. Fig. 5a,b] were fitwith the same τ−1i and τ−1∗ values, while τ−1ϕ (T ) was extracted for each tempera-ture. Accuracy of the extracted τϕ(T ) was improved by fitting both narrow [section(a) of Figure 7.2, Figure 7.3 and Figure 7.4] and broader [section (b) of Figure 7.2,Figure 7.3 and Figure 7.4] magnetic field ranges using the same rates. As ex-pected from Equation 2.7, the extracted τ−1ϕ (T ) is indeed linear in T, with a sig-nificant offset that may be attributed to spin impurities of SiC samples [section (c)of Figure 7.2, Figure 7.3 and Figure 7.4]. Considering the temperature-dependentτ−1ϕ (T ), and temperature-independent valley scattering rates, the net weak localiza-780.∆σ(e2 /h)1050-5-10B (mT)2.8 K4.4 K6.5 K(a)∆σ(e2 /h)-100 0 100B (mT)(b)480440400360τ φ−1(x109s-1 )765432T (K)(c)80.079.679.2σ-σ WL(e2 /h)2 3 4 5 6 7 8 9T (K)(d)Figure 7.4: (a,b) Narrow and broad magnetic field ranges for the magneto-conductivity of the pristine SiC4 graphene device which was annealedto 500 K one time, 700 K two times, doped by Li and exposed to airprior to cooldown in UHV chamber, showing fits to Equation 2.6. (c)Extracted dephasing rate τ−1ϕ (T ), with linear fit. (d) Graphene conduc-tivity after subtracting the contribution due to weak localization, withlinear-log fit.tion contribution to conductivity can be subtracted [173, 174] for each temperature[section (d) of Figure 7.2, Figure 7.3 and Figure 7.4]. What remains is the electron-electron suppression of conductivity, which is proportional to ln(T ), as expectedin any 2D metal[173–175]:< σ >= σ0+Ae2pihlnT (7.1)where A is a coefficient which depends on e-e interaction strength and the symme-try of electron states[173]. Taken together, the non-saturating temperature depen-dences observed in sections c and d of of Figure 7.2, Figure 7.3, and Figure 7.4,from 9 K down to about 3 K, offer strong evidence that the electronic temperaturefollows the substrate temperature well below 4K.797.3 DiscussionHow can we understand the lack of a resistivity downturn as low as 3 or 4 K forLi-doped graphene, while Ref. [24] predicted a TC=8.1 K and Ref. [49] reportedevidence of a temperature-dependent pairing gap corresponding to a TC '5.9 K?We consider three possibilities:1. The transition to superconductivity in quasi-2D films is governed by su-perconducting fluctuations [94, 176], and is not as abrupt as it is for 3Dmaterials. It is in principle possible that a gradual reduction in resistancewith decreasing T could be hidden on top of the increasing resistance dueto weak localization and electron-electron interactions. In that case, how-ever, one would expect significantly modified magnetoresistance curves, re-flecting weak localization on top of magnetic field suppression of incipientsuperconductivity. This was not observed.2. Thermal fluctuations can suppress superconductivity in 2D systems via theBerezinskii-Kosterlitz-Thouless (BKT) transition. In this case, a system maypossess a pseudogap without showing any suppression of resistance [177–179]. The BKT scenario has been observed experimentally for proximity-induced superconductivity on graphene [180, 181], and predicted theoreti-cally for superconductivity in doped graphene [178]. To estimate the im-portance of this effect, we use an expression for the BKT transition tem-perature that is well established in metals: kBTBKT = dΦ20ρc/8piµ0 whered is the graphene thickness, Φ0=h/2e is the flux quantum, and ρc is thesuperfluid density[177, 182]. Using Homes’ law[183] to estimate super-fluid density in the SiC sample after Li deposition, ρc ∼ 120σNTc/d whereσN = 0.007 is the normal state 2D conductivity in Ω−1, d = 3.4× 10−8 isthe graphene’s “thickness” in cm, and Tc = 5.9 K is the critical temperature,we find ρc ∼ 1.5× 108 cm−2 gives TBKT ∼ 5 K. Given the significant ap-proximations involved in the above calculation, the fact that Tc and TBKT areso similar shows that a BKT-induced suppression of Tc must be considered,calling for further measurements at significantly lower temperatures.3. ARPES-detected signatures of superconductivity due to Li adatoms were ob-80served only for some SiC samples, and only after repeated annealing opera-tions monitored by the sharpness of the graphene band structure [184]. It ispossible that superconductivity by Li adatoms requires a specific graphenecondition that was not realized in our experiments. The SiC data reportedhere are not for the specific chip used in Ref. [49]. We first measuredthat chip but found an extremely anisotropic resistance; the SiC1 samplereported here was grown later in the same chamber, aiming for more optimalgrowth parameters. Unfortunately, due to the low resistance of SiC1 sub-strate at room temperature, it was not possible to anneal its graphene in ourheater stage. For performing high-temperature annealing, we used SiC2,3,4that were cut from a commercially available epitaxial monolayer graphene.These samples can be grown in different conditions from SiC1.81Chapter 8Two Heavy Metal Candidates forEnhancing Spin-orbit Interactionin Graphene: Indium and CopperHeavy metal adatoms indium (In) and copper (Cu) are two candidates for enhanc-ing spin-orbit interaction in graphene. As explained in Section 2.7, it is predictedtheoretically that deposition of In may enhance spin-orbit coupling to the pointwhere graphene becomes a quantum spin Hall insulator [28, 31, 32]. A modest6% coverage of In, which has a hollow configuration and partially filled p shell,could produce dominant Kane-Mele spin-orbit coupling with λKM =3.5 meV [28].Another theoretical report predicts that 1% coverage of Cu adatoms on graphene,in top position, induces both Bychkov-Rashba and Kane-Mele spin-orbit couplingwith strengths of λBR =30 meV and λKM =9 meV [113]. There is an experimentalreport of observing spin-orbit strength of the range 6.4-8.7 meV on copper-dopedgraphene by non-local measurements (i.e. sending current through two contactsand measuring non-local voltage at two other contacts with some distant from cur-rent pads). They conclude that the Kane-Mele type is dominant, not the Bychkov-Rashba [119]. It should be pointed out that there is no discrepancy between theresult of this experiment and the theory. Because while the theory is about sin-gle isolated copper adatoms on graphene [113], the mentioned experimental reportstudied the effect of copper clusters on graphene [119]. However, using non-local82measurements as an evidence of spin-orbit interaction has been criticized, becausethe non-local signal may have a valley source and not necessarily spin [117]. Weaklocalization study can differentiate between valley and spin and solve this prob-lem. Another weakness of that experimental report is that only graphene samplesalready doped with copper (either CVD with Cu contamination or Cu-doped exfoli-ated graphene made in a solution) were measured [119]. There was not a measure-ment for the same pristine sample without copper for comparison. Considering thisbackground, we studied the effect of Cu and In deposition on graphene transportproperties as will be described in this chapter. We tried to improve the experimen-tal study on copper-doped graphene by probing weak localization on monolayergraphene before and after copper deposition. However, experimental signatures ofinducing magnetic moments and Kane-Mele spin-orbit interaction are similar inweak localization for copper adatoms, making a clear interpretation of this experi-ment difficult.Measurements of this chapter were performed on four different exfoliated de-vices: EXF1,2,3 on SiO2/Si and EXF-BN on boron nitride (BN)/SiO2/Si. High-temperature annealing was not performed on any of these samples. Further detailsabout the samples are provided in Section Indium-doped GrapheneFigure 8.1 (a) shows 2-probe Dirac peak measurements of EXF-BN, which was anexfoliated graphene sample on a BN substrate [See Section 4.1 and Figure 4.1 (e)],before and after deposition of 0.002 monolayers (ML) of In (i.e. 2 indium atomsper 1000 unit cell or 3.3× 1012 In atoms per cm2) [For details of evaporation,see Section 3.10]. Density of In adatoms on the graphene surface was measuredusing a crystal monitor. Both deposition and measurement were performed at 6 K.The high resistance at the Dirac peak was due to the sample geometry (5 squares).As seen in Figure 8.1 (a), spatial charge inhomogeneity introduced by In adatomsbroadened the Dirac peak and decreased the mobility. As a result of In deposition,maximum resistivity decreased (i.e the minimum conductivity increased). It isworthwhile to note that In is a group III metal in the periodic table. As discussedin Section 2.4, the group III metal adatoms act as both long-range and short-range83(a)70605040302010R (kΩ)µe~2000±1500 cm2/VsMax R=44kΩFWHM=33 VAfter In Dep.(0.002ML)Before In Dep.∆VBG=38V∆EF=0.27eV µe~4000±1300 cm2/VsMax R=75kΩFWHM=4 V40302010-40 -20 0∆VBG=29V;∆EF=0.24eVµe~2000±1500 cm2/VsDP=-40VMax R=44kΩFWHM=33 Vµe~3500±300 cm2/VsDP=-11VMax R=39kΩFWHM=20 VVbg (V)20R (kΩ)(b)Figure 8.1: (a) The effect of 0.002 ML In deposition on graphene sampleEXF-BN at 6 K. (b) Changes in resistivity curve upon temperature cy-cling, which indicates clustering.scatterers [3, 4, 43, 61]. Moreover, charge transfer from In was consistent withtheoretical predication of η=0.8 for In adatom [28].After warming to room temperature, then recooling to 6 K, the net chargetransfer was reduced [Figure 8.1 (b)] and mobility slightly increased. Reducingdoping and increasing mobility indicate irreversible cluster formation at temper-atures large enough that In atoms can move around on the graphene. This phe-nomenon was also reported for Au and Gd adatoms [36, 37]. More In deposition8440353025201510-25 -20 -15 -10 -5 0 5 10∆VBG=10V;∆EF=0.14eVµe~2200±1000 cm2/VsDP=-18VMax R=40kΩFWHM=22 Vµe~3500±300 cm2/VsDP=-8VMax R=37kΩFWHM=20 V0.0004 ML Dep.R (kΩ)Vbg (V)Figure 8.2: More In deposition on EXF-BN after temperature cycling.on EXF-BN, after temperature cycling, shifted the Dirac peak to more negative gatevoltages, consistent with the theoretical prediction of η=0.8 [Figure 8.2]. Similarresults were observed in a separate experiment of deposition of In on a three-layergraphene on SiO2 substrate, though in this case the deposition and measurementswere performed at 77 K. After the end of the experiment on the In-doped three-layer graphene, we brought the sample to air and imaged it with a Scanning Elec-tron Microscope (SEM). As can be seen in Figure 8.3, the In adatoms made ∼20nm clusters on the graphene surface.Unfortunately, our setup was not equipped with a magnet at the time of the Inexperiment. Therefore, we were not able to run magnotoresistance measurementson In-doped graphene to look for enhanced spin-orbit interaction [28, 31, 32].However, two other experimental groups looked at this effect in In-doped grapheneand did not observe any sign of spin-orbit interaction enhancement [33, 34]. As dis-cussed in Chapter 5, this may be related to the fact that reliable adatom-grapheneinteractions can be achieved only after in situ high-temperature annealing proce-dures. Graphene on SiC samples are not ideal for enhancement of spin-orbit in-teraction measurements, due to their higher dephasing rate compared to exfoliatedgraphene on SiO2. We suggest using 900/700 K annealed exfoliated samples on85Figure 8.3: SEM images of In clusters on three-layer graphene surface.86boron nitride substrate to avoid degrading effects that was observed for exfoliatedgraphene on SiO2 substrate after high-temperature annealing [162]. It is also idealif the graphene contacts could be placed by shadow mask evaporation and not usingpolymer resists, to avoid polymer residue on the sample.To summarize, the cryogenic deposition of indium (In) doped graphene witheach In adatom donating 0.8e to graphene, consistent with theoretical prediction[28]. This deposition also decayed the mobility and maximum resistance of thegraphene device. Warming the sample to room temperature caused an irreversiblecluster formation which showed itself in transport measurements by reducing dop-ing and increasing mobility after recooling. Our suggestion for detecting enhance-ment of spin-orbit interaction in Li-doped graphene is to use high-temperature an-nealed exfoliated samples on boron nitride substrate with contacts deposited byshadow mask evaporation.8.2 Copper-doped Graphene8.2.1 Trying to Evaporate Iridium Which Turned out to be CopperWe tried to evaporate iridium (Ir) on graphene and probe its effect. For this goal,we used an Iridium (Ir) coil made from Ir wire with diameter of 0.25 mm connectedto two copper current leads. Two 4-probe exfoliated graphene devices (EXF1 andEXF2) on SiO2 substrate [See Section 4.1 and Figure 4.1 (a), (b) and (c)] wereused for these measurements. After the end of the experiment, we probed thedoped graphene sample EXF1 by time-of-flight secondary ion mass spectrometry(ToF-SIMS) to confirm the presence of Ir. While we found clear presence of Cu,the presence of Ir was questionable [See Figure 8.4]. The probable explanation isthe Ir coil heated the copper current leads and resulted in evaporation of copper,which needed much less temperature to evaporate compared to Ir. Note that allof the coverage in the following graphs in this section were measured by crystalmonitor, assuming density and acoustic impedance of Ir. If we assume all of thedeposition was Cu, the coverage would be 2.5 times more in each deposition (e.g.,0.03ML Ir=0.75 ML Cu). However, if we had a mixture of both Cu and Ir, thenthe calculated adatom coverage would be something in between, depending on the87Figure 8.4: ToF-SIMS’s positive mode image of EXF1 after deposition bydifferent ion and possible trace of Ir on the surface of sample. The Niand Au picture shows the electrical contacts of the sample.exact ratio of these two adatoms.Figure 8.5 illustrates the effects of this deposition observed during three sepa-rate measurements on these two devices. Figure 8.5 (c) shows adatoms moving theDirac peak by giving a fraction of electron charge to graphene (η), until it reachesa saturation. Considering the region before saturation in Figure 8.5, η for sup-posedly Ir atoms is 0.03±0.01, which is much less than the theoretically predictedamount for Ir (η = 0.22) [185].Figure 8.6 (a) and (b) demonstrate magnetoconductivity of EXF1 before andafter adatom deposition. All measurements were done at the same charge carrierdensity of n = 4.85± 0.05× 1012 cm−2 (i.e. ∆Vg,min ' 64 V), to make the com-parison reasonable. Furthermore, the horizontal axis is converted to units of rate,through the diffusion constant (τ−1B = B(4eD/h¯)), to omit the effects of changingthe diffusion constant which can be seen in Figure 8.6 (c). The noticeable change inmagnetoconductivity after adatom deposition, especially the change in curvature,suggests a significant increase of dephasing rate.To understand the meaning of dephasing rate increase, we need to know what is88(a) (b)1201008060402006040200-20-400ML0.0007ML0.0070ML0.0300ML0.0700ML5040302010σ(e2/h)-40 -20 0 20 40Vbg (V)0ML0.0008ML0.0064ML0.0230ML0.0396ML0.0563ML0.0660MLσ(e2/h)Vbg (V)EXF1EXF2302520151050∆Vg,min(V) (ML)EXF1 (7-8 K)EXF2 (8-12 K)EXF2 (90-100 K)line for Ir chargetransfer of 0.03e(c)Figure 8.5: (a) Conductivity (σ ) versus back gate voltage (Vbg) for pristineand doped graphene with different adatom coverages for two differentsamples at 8-12 K. (b) The gate voltage shift of minimum conductivityVg,min upon adsorption of adatom vs. coverage of adatoms (as fractionsof a monolayer) for two different graphene devices at different temper-atures.the deposited metal. Due to the ambiguity of copper coverage in this experiment,we decided to test the effect of deposition of copper alone to find out whethercopper is responsible for the increasing of dephasing rate in doped graphene. Wewill discuss this experiment in the next section.8.2.2 Deposition of CopperCu was deposited on EXF3 using the alumina-coated tungsten basket described inSection 3.10. The effect of Cu deposition on the Dirac peak is shown in Figure 8.7.The Dirac peak (DP) of pristine graphene can not be seen in the picture. However,Hall measurements of density show that DP should be at 96 V. In Cu depositions890.{σ(B)-σ(0)} (e2/h)τB (1012s-1)0ML0.0300ML0.0700ML1. -5 0 5 100ML0.0300ML0.0700ML1/τB (1012s-1){σ(B)-σ(0)} (e2/h)440420400380360340D (cm2/s) (ML)n=5×1012 cm-2(c)(b)(a)Figure 8.6: (a) and (b) Magnetoconductivity of graphene flake EXF1 for pris-tine graphene and after varying amounts of adatom deposition. (c) Dif-fusion constant of EXF1 versus adatom coverage.902520151050Rxx (kΩ)806040200-20-40-60Vbg (V) 0ML 0.0744ML 0.0992ML 0.1488ML 0.2381MLFigure 8.7: Dirac peak shift with consecutive Cu depositions on EXF3 at 4.4K.after the first deposition, the shift of DP was slowed down. The charge transfer ofCu was found η = 0.05 in the first deposition, which is lower than theoreticallypredicted η ≈ 0.2 [113, 186]. This is probably a sign that the saturation alreadystarted during the first deposition. Another sign of saturation is the DP shift. Whilethe DP shifted around 90 V after the first copper deposition (7%), during the laterdeposition steps the coverage reached 14% but the DP just shifted around 30 V andafter that, it stopped shifting and doping was apparently saturated. It shows thatthe sample was at the verge of saturation even at the first deposition.Figure 8.8 (a) and (b) demonstrate magnetoconductivity of EXF3 before andafter adatom depositions. All measurements were done at the same charge car-rier density of n = 4× 1012 cm−2 (i.e., ∆Vg,min ' 60 V), to make the comparisonreasonable. Furthermore, the horizontal axis is converted to units of rate, throughthe diffusion constant (τ−1B = B(4eD/h¯)), to omit the effects of the changing dif-fusion constant [Figure 8.8 (c)]. The noticeable change in magnetoconductivityafter copper deposition, especially the decrease in curvature, suggests a significantincrease of the dephasing rate and characteristic dephasing field. As can be seen in910.∆σ(e2 /h)-2 -1 0 1 21/τB(x1015 s-1)0ML0.0744ML0.1488ML(a)∆σ(e2 /h)-20 -10 0 10 201/τB(x1015 s-1)(b)400350300250200150D (cm2 /s) (ML)n=4×1012 cm-2(c)Figure 8.8: (a) and (b) Magnetoconductivity of graphene flake EXF3 for pris-tine graphene and after varying amounts of copper deposition. (c) Dif-fusion constant of EXF3 versus copper coverage.92Table 8.1: Characteristic fields extracted from fitting Equation 2.6 to the mag-netoconductivity curves in Figure 8.8 (a) and (b).Cu Coverage Bϕ (mT) Bi (mT) B∗ (mT)0 ML 0.5±0.01 2±0.1 24±10.0744 ML 1.3±0.01 8±7.9 16±90.1488 ML 2.3±0.02 8±4.9 11±10Table 8.1, fitting Equation 2.6 to the magnetoconductivity curves in Figure 8.8 (a)and (b) confirms this increase. Accuracy of the extracted Bϕ was improved by fit-ting both narrow [Figure 8.8 (a)] and broader [Figure 8.8 (b)] magnetic field rangesusing the same characteristic fields.The observed increase of Bϕ might be explained by copper adatoms induc-ing magnetic moments. On the other hand, it is not expected that magnetic mo-ments would be induced by Cu clusters. While the copper adatoms adsorbed ongraphene exhibit local magnetic moments, copper dimers do not show any mag-netism [12, 187]. If there is an odd number of copper atoms in the cluster one canexpect a magnetic moment, although this magnetic moment spreads over the com-plete cluster. Therefore, the coupling/transfer of the magnetic moment to grapheneis smaller the more (odd number of) copper atoms the cluster holds. One couldthen expect from this argument that for large clusters the magnetic moment is lessimportant [188]. While we observed saturation of charge carrier density, we cannotbe sure that it was caused by clusters of copper atoms on graphene. Due to our lowcoverage of copper, there is a strong possibility of residual isolated copper atomson the graphene, which can induce magnetic moments.Another possible explanation for increased dephasing rate/characteristic fieldis enhancement of spin-orbit interaction by copper deposition. Assuming no induc-tion of magnetic moments by copper, Equation 2.19 can be used for fitting to themagnetoconductivity curves of copper-doped graphene in Figure 8.8 (a) and (b).Table 8.2 shows the extracted characteristic fields from these fits. Similar valuesof BKM and BBR, their large error bars, and the normalized chi-square values, χ2v ,which show the goodness of fits [For definition of χ2v , see Chapter 6], all demon-strate the fact that BKM and BBR are indistinguishable and can be replaced by each93Table 8.2: Characteristic fields extracted from fitting Equation 2.19 to themagnetoconductivity curves in Figure 8.8 (a) and (b). While the thirdand fourth rows show the extracted characteristic fields when BBR forcedto be zero, the fifth and sixth rows show the extracted characteristic fieldswhen BKM forced to be zero. The last column shows the normalized chi-square values, χ2v .Cu Coverage Bϕ (mT) Bi (mT) B∗ (mT) BKM (mT) BBR (mT) χ2v0.0744 ML 0.5±0.07 8±5.5 12±10 0.1±0.09 0.2±0.05 0.780.1488 ML 1.5±0.51 9±8.0 10±9 0.21±0.73 0.3±0.39 1.880.0744 ML 1.0±0.90 8±5.3 11±9 0.4±0.16 0±0 0.800.1488 ML 1.5±0.41 8±5.4 12±11 0.8±0.41 0±0 1.900.0744 ML 0.5±0.03 8±4.9 11±10 0±0 0.3±0.01 0.780.1488 ML 1.5±0.40 7±1.7 15±5 0±0 0.4±0.16 1.90other. This means that it is possible to have a good fit with both Kane-Mele andBychkov-Rashba spin-orbit interactions or just with one of them.8.3 ConclusionTo summarize Section 8.2.1 and Section 8.2.2, cryogenic deposition of copper in-creased the dephasing rate/characteristic field of graphene, which is either a signof inducing spin-orbit interaction or magnetic moments by copper.Unlike copper, indium-doped graphene does not show any sign of increasingof dephasing rate. The lack of spin-orbit interaction enhancement in indium-dopedgraphene [33, 34] may be related to the fact that reliable adatom-graphene inter-actions can be achieved only after in situ high-temperature annealing procedures[See Chapter 5]. Using 900/700 K annealed exfoliated samples on boron nitridesubstrate might solve this inconsistency with theory.94Chapter 9ConclusionsThis thesis investigated the effects of cryogenic deposition of alkali (Li) and heavy(In and Cu) adatoms on the transport properties of electrons in different types ofgraphene (epitaxial, CVD, exfoliated). To this end, a rather unique experimentalsetup was designed and built. The setup allowed us evaporate metal adatom ongraphene at cryogenic temperatures in UHV, apply variable perpendicular magneticfield between -100 and 100 mT, and perform high-temperature (up to 1000 K)annealing on graphene samples prior to cryogenic deposition (Chapter 3).One of the primary conclusions of this research is that it is really hard to achievereliable interaction between adatoms and graphene surface. The usual 300-400 Kannealing of graphene sample in UHV is not enough for acquiring this reliableinteraction. Chapter 5 demonstrated the critical role of in situ high-temperatureannealing in creating reliable adatom-graphene interactions. Even charge dopingby alkali atoms (Li), which is arguably the simplest of all adatom effects, dependson this interaction. Annealing the graphene prior to cryogenic deposition greatlyenhanced the maximum levels of doping from saturation after nearly 10 % Li cov-erage without annealing to saturation after nearly 100 % Li coverage with a 900K anneal prior to cryogenic deposition. This observation can explain the inconsis-tency between theory and experiment in inducing theoretically predicted electronicmodifications such as spin-orbit interaction and superconductivity to graphene byadatom deposition. We suggest that high-temperature annealing may solve thisproblem.95Another important result of this research breaks the naive picture of alkaliadatoms as a source of only long-range scattering in graphene. We present the firstexperimental evidence of short-range scattering from alkali adatoms in grapheneand its effect on enhancement of intervalley scattering (Chapter 6). According tothis revised picture, alkali atoms act as both long-range and short-range scattererson graphene. In addition to different types of scatterings, the theoretically pre-dicted superconductivity of Li doped graphene was investigated. No signatures ofsuperconductivity were observed down to 3 K (Chapter 7).Finally, the effect of indium and copper deposition on graphene exfoliated sam-ples was probed (Chapter 8). Both adatoms have been suggested as candidates forenhancing spin-orbit coupling in graphene. The observed increase of dephasingrate after copper deposition is either a sign of inducing spin-orbit interaction ormagnetic moments. However, the lack of dephasing rate enhancement in indium-doped graphene should not be interpreted as inaccuracy of theories. It is rather asign that experiments require further preparation steps such as high-temperatureannealing to acquire reliable adatom-graphene interactions.96Bibliography[1] A. Khademi, E. Sajadi, P. Dosanjh, D. A. Bonn, J. A. Folk, A. Sto¨hr,U. Starke, and S. Forti, Phys. Rev. B 94, 201405 (2016), URL → pages v, 56, 64[2] K. S. 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Lett. 10, 486 (1963), URL → pages 138[194] V. Ambegaokar and A. Baratoff, Phys. Rev. Lett. 11, 104 (1963), URL → pages 138[195] F. Miao, W. Bao, H. Zhang, and C. N. Lau, Solid State Communications149, 1046 (2009), ISSN 0038-1098, recent Progress in Graphene Studies,URL →pages 138115Appendix ADetailed Design of ExperimentalSetupThis appendix explains the details of our experimental setup design, constructionand assembly that are not essential for understanding the main arguments of thethesis. However, this information can be very helpful for designing similar experi-ments.A.1 Magnet FrameThe first custom-built copper part was a magnet frame, which acts as both magnetframe and a part of 4 K shield. A series of taped screw holes were placed on thetop of part to let two other copper cup shape parts (bottom connector and sampleholder) be screwed to this part [See Figure A.1 and Figure A.2].For holding magnet frame temporarily during wire winding, an aluminum holderwas also made [See Figure A.3]. Figure A.4 shows the magnet frame on this holder.A.2 Winding Superconducting Wire for MagnetFor wire winding, a T48B-M superconducting wire (Cu:Sc=1.5:1, with bare diam-eter of 79 µm and Formvar insulated diameter of 104 µm) made by ”SuperconInc.” was wound 465 turns using a winding machine as it shown in Figure A.5. Atwo component, thermally conductive, electrically insulating epoxy named EPO-1161.4171.000.243.743.089.0701.256.984.039.211.315 for 4-40screwsAlignment Rod1.693.866.089.079Tapped for 4-40screwsAlignment RodDO NOT SCALE DRAWINGMFSHEET 1 OF 1UNLESS OTHERWISE SPECIFIED:SCALE: 1:2 WEIGHT: REVDWG.  NO.ASIZETITLE:NAME DATECOMMENTS:Q.A.MFG APPR.ENG APPR.CHECKEDDRAWNFINISHMATERIALINTERPRET GEOMETRICTOLERANCING PER:DIMENSIONS ARE IN INCHESTOLERANCES:FRACTIONALANGULAR: MACH      BEND TWO PLACE DECIMAL    THREE PLACE DECIMAL  APPLICATIONUSED ONNEXT ASSYPROPRIETARY AND CONFIDENTIALTHE INFORMATION CONTAINED IN THISDRAWING IS THE SOLE PROPERTY OF<INSERT COMPANY NAME HERE>.  ANY REPRODUCTION IN PART OR AS A WHOLEWITHOUT THE WRITTEN PERMISSION OF<INSERT COMPANY NAME HERE> IS PROHIBITED.5 4 3 2" deepDO NOT SCALE DRAWINGMF2SHEET 1 OF 1UNLESS OTHERWISE SPECIFIED:SCALE: 1:2 WEIGHT: REVDWG.  NO.ASIZETITLE:NAME DATECOMMENTS:Q.A.MFG APPR.ENG APPR.CHECKEDDRAWNFINISHMATERIALINTERPRET GEOMETRICTOLERANCING PER:DIMENSIONS ARE IN INCHESTOLERANCES:FRACTIONALANGULAR: MACH      BEND TWO PLACE DECIMAL    THREE PLACE DECIMAL  APPLICATIONUSED ONNEXT ASSYPROPRIETARY AND CONFIDENTIALTHE INFORMATION CONTAINED IN THISDRAWING IS THE SOLE PROPERTY OF<INSERT COMPANY NAME HERE>.  ANY REPRODUCTION IN PART OR AS A WHOLEWITHOUT THE WRITTEN PERMISSION OF<INSERT COMPANY NAME HERE> IS PROHIBITED.5 4 3 2 1Figure A.1: Drawing of magnet frame.117Figure A.2: Photograph of magnet frame..070.500.252.548.878.207Threaded hole for 2-56 screw.970.7001.3001.400R.7001.292.270Aluminum PartDO NOT SCALE DRAWINGAl HolderSHEET 1 OF 1UNLESS OTHERWISE SPECIFIED:SCALE: 1:1 WEIGHT: REVDWG.  NO.ASIZETITLE:NAME DATECOMMENTS:Q.A.MFG APPR.ENG APPR.CHECKEDDRAWNFINISHMATERIALINTERPRET GEOMETRICTOLERANCING PER:DIMENSIONS ARE IN INCHESTOLERANCES:FRACTIONALANGULAR: MACH      BEND TWO PLACE DECIMAL    THREE PLACE DECIMAL  APPLICATIONUSED ONNEXT ASSYPROPRIETARY AND CONFIDENTIALTHE INFORMATION CONTAINED IN THISDRAWING IS THE SOLE PROPERTY OF<INSERT COMPANY NAME HERE>.  ANY REPRODUCTION IN PART OR AS A WHOLEWITHOUT THE WRITTEN PERMISSION OF<INSERT COMPANY NAME HERE> IS PROHIBITED.5 4 3 2 1Figure A.3: Drawing of aluminum holder for magnet frame.118Figure A.4: Photograph of magnet frame on its aluminum holder.119Figure A.5: Photograph of winding superconducting wire for magnet.120Figure A.6: Photograph of winded magnet and its solder joints.TEK H77 was used for filling space between superconducting wire turns and makea good thermal connections to help cooling the magnet wires. After finishing wirewinding, two piece of 22 AWG kapton insulated silver plated copper wires madeby Accuglass (part number: 100680) were soldered to the two ends of supercon-ducting wire. One of copper wires was wrapped on magnet for half a turn. Finallysolder joints were covered by H77 epoxy and epoxy was cured by a table lamp [SeeFigure A.6].A.3 Sample Holder and Bottom ConnectorFor placing sample in the middle of magnetic field produced by the superconduct-ing magnet, a cup-shaped copper piece was made with 9 holes for 9 male pins [SeeFigure A.7 and Figure A.10]. For electrical connection, these 9 male pins are plug-ging into 9 female pins on another cup-shaped copper on the bottom with 9 holesfor these female pins [See Figure A.8 and Figure A.10]. After plugging sampleholder inside bottom connector, the sample covered from top with a cover platewith a hole in its middle for adatom deposition [See Figure A.9 and Figure A.10].121.1321.693.730.709. clear holes for 4-40 screws4 clear holes for 2 mm diameter alignment rods2 threaded holes for 2-56 screws2 threaded holes for 2-56 screwsDO NOT SCALE DRAWINGS HolderSHEET 1 OF 1UNLESS OTHERWISE SPECIFIED:SCALE: 1:1 WEIGHT: REVDWG.  NO.ASIZETITLE:NAME DATECOMMENTS:Q.A.MFG APPR.ENG APPR.CHECKEDDRAWNFINISHMATERIALINTERPRET GEOMETRICTOLERANCING PER:DIMENSIONS ARE IN INCHESTOLERANCES:FRACTIONALANGULAR: MACH      BEND TWO PLACE DECIMAL    THREE PLACE DECIMAL  APPLICATIONUSED ONNEXT ASSYPROPRIETARY AND CONFIDENTIALTHE INFORMATION CONTAINED IN THISDRAWING IS THE SOLE PROPERTY OF<INSERT COMPANY NAME HERE>.  ANY REPRODUCTION IN PART OR AS A WHOLEWITHOUT THE WRITTEN PERMISSION OF<INSERT COMPANY NAME HERE> IS PROHIBITED.5 4 3 2 1Figure A.7: Drawing of sample holder..8271.693.1521. Clear holes for 4-40 screw 4 Clear holes for alignment rodsDO NOT SCALE DRAWINGB ConnectorSHEET 1 OF 1UNLESS OTHERWISE SPECIFIED:SCALE: 1:1 WEIGHT: REVDWG.  NO.ASIZETITLE:NAME DATECOMMENTS:Q.A.MFG APPR.ENG APPR.CHECKEDDRAWNFINISHMATERIALINTERPRET GEOMETRICTOLERANCING PER:DIMENSIONS ARE IN INCHESTOLERANCES:FRACTIONALANGULAR: MACH      BEND TWO PLACE DECIMAL    THREE PLACE DECIMAL  APPLICATIONUSED ONNEXT ASSYPROPRIETARY AND CONFIDENTIALTHE INFORMATION CONTAINED IN THISDRAWING IS THE SOLE PROPERTY OF<INSERT COMPANY NAME HERE>.  ANY REPRODUCTION IN PART OR AS A WHOLEWITHOUT THE WRITTEN PERMISSION OF<INSERT COMPANY NAME HERE> IS PROHIBITED.5 4 3 2 1Figure A.8: Drawing of bottom connector.122.3941.654. 2 clear holes for 2-56 screws8 clear holes for 4-40 screws4 clear holes for 2mm diameter alignment rodsThickness of cover plate is 0.059"DO NOT SCALE DRAWINGCoverSHEET 1 OF 1UNLESS OTHERWISE SPECIFIED:SCALE: 1:1 WEIGHT: REVDWG.  NO.ASIZETITLE:NAME DATECOMMENTS:Q.A.MFG APPR.ENG APPR.CHECKEDDRAWNFINISHMATERIALINTERPRET GEOMETRICTOLERANCING PER:DIMENSIONS ARE IN INCHESTOLERANCES:FRACTIONALANGULAR: MACH      BEND TWO PLACE DECIMAL    THREE PLACE DECIMAL  APPLICATIONUSED ONNEXT ASSYPROPRIETARY AND CONFIDENTIALTHE INFORMATION CONTAINED IN THISDRAWING IS THE SOLE PROPERTY OF<INSERT COMPANY NAME HERE>.  ANY REPRODUCTION IN PART OR AS A WHOLEWITHOUT THE WRITTEN PERMISSION OF<INSERT COMPANY NAME HERE> IS PROHIBITED.5 4 3 2 1Figure A.9: Drawing of cover plate.A.4 Gluing Male and Female Pins to Sample Holder andBottom ConnectorFor the purpose of gluing male pins to sample holder and also holding sampleholder without damaging its pins, an aluminum part was made [See Figure A.11and Figure A.12]Figure A.13 shows the copper alloy, gold-plated male and female pin contactswere bought from ”Accu-Glass Product Inc.” (Part numbers: 100170 and 100180).First, before placing pins inside sample holder and bottom connector, the middleof each pin’s body was covered by insulating H77 epoxy to prevent short-circuit.Then the sample holder was placed inside its aluminum holder using screws andmale pins were placed inside its holes as it shown in Figure A.14], then the holeswere filled by H77 epoxy and cured in different steps. The height of aluminumholder designed to place the male pins exactly at the suitable position for laterplugging into female pins in bottom connector. After filling the holes from top sideand making sure that they are strong enough and not shorted to the body of sample123Figure A.10: Photograph of sample holder, bottom connector, and coverplate.holder, the sample holder was removed from its aluminum holder and the holeswere filled by H77 epoxy from back side as well and sample holder was curedagain. Figure A.15 shows the finally made sample holder. As it can be seen in thatfigure, there are some windows on the sample holder to make space for workingon sample.For pasting female pins to the bottom connector, again the middle of femalepins’ body were covered by H77 epxoy. For holding them, we used fixed malepins that were glued to the sample holder [See Figure A.16]. In the next step, weput them inside the holes of the bottom connectors and soldered 34 AWG kaptoninsulated silver-plated copper wires from ”Accu-Glass Product Inc.” (part num-124.152.732.157.8681.693.089.089.732.827.041Threaded holes for 4-40 screwsAluminum Part for Sample Holder DO NOT SCALE DRAWINGAl PartSHEET 1 OF 1UNLESS OTHERWISE SPECIFIED:SCALE: 1:1 WEIGHT: REVDWG.  NO.ASIZETITLE:NAME DATECOMMENTS:Q.A.MFG APPR.ENG APPR.CHECKEDDRAWNFINISHMATERIALINTERPRET GEOMETRICTOLERANCING PER:DIMENSIONS ARE IN INCHESTOLERANCES:FRACTIONALANGULAR: MACH      BEND TWO PLACE DECIMAL    THREE PLACE DECIMAL  APPLICATIONUSED ONNEXT ASSYPROPRIETARY AND CONFIDENTIALTHE INFORMATION CONTAINED IN THISDRAWING IS THE SOLE PROPERTY OF<INSERT COMPANY NAME HERE>.  ANY REPRODUCTION IN PART OR AS A WHOLEWITHOUT THE WRITTEN PERMISSION OF<INSERT COMPANY NAME HERE> IS PROHIBITED.5 4 3 2 1Figure A.11: Drawing of aluminum part for sample holder.Figure A.12: Photograph of aluminum part for sample holder.125Figure A.13: Photograph of male and female pin contacts.Figure A.14: Photograph of sample holder and its male pins placed insidealuminum part, ready for gluing.126Figure A.15: Photograph of final sample holder with its glued male pins.ber: 110824) to the solder cup of female pins [see Figure A.17 and Figure A.18].Then, we glued them to the holes with H77 epoxy [see Figure A.19]. Finally, wetwisted the wires and made them springy to be easy to put it later inside the magnetframe. We covered the end of wires with black ECCOSORB CR-124 epoxy [seeFigure A.20].127Figure A.16: Photograph of female pins covered by H77 epoxy in their mid-dle on top of sample holder’s male pins.Figure A.17: Soldering wires to female pins under the microscope.128Figure A.18: Photograph of wires soldered to female pins.Figure A.19: Gluing female pins with H77 epoxy to the bottom connector.129Figure A.20: Photograph of twisted wires connected to female pins in bottomconnector.A.5 30 K Outer ShieldIn addition to magnet frame, which acts as a 4 K shield, a copper outer radia-tion shield was designed to surround everything include magnet frame and sampleholder. This outer shield is actually continuation of the 30 K gold-plated radia-tion shield made by company. A copper adapter and eight 2-56 titanium screwswere used to connect these two shields [See Figure A.21]. Figure A.22 shows thegold-plated shield with adapter installed on it. The outer shield is a cylinder with acircular hole in the middle of its base [See Figure A.23 and Figure A.24]. The holelet evaporated adatoms reach the sample. Two additional parts was also attached tothe outer shield to make a path for shutter sliding to open and close the hole [SeeFigure A.25]. A piece of copper braid glued to another attached part to make athermal connection between outer shield and shutter.1300.1970.3940.3541.8901.5574 clear holes for 2-56 screws4 threaded holes for 2-56 screws1.4001.8900.0700.0390.0891.557DO NOT SCALE DRAWINGAdapterSHEET 1 OF 1UNLESS OTHERWISE SPECIFIED:SCALE: 1:1 WEIGHT: REVDWG.  NO.ASIZETITLE:NAME DATECOMMENTS:Q.A.MFG APPR.ENG APPR.CHECKEDDRAWNFINISHMATERIALINTERPRET GEOMETRICTOLERANCING PER:DIMENSIONS ARE IN INCHESTOLERANCES:FRACTIONALANGULAR: MACH      BEND TWO PLACE DECIMAL    THREE PLACE DECIMAL  APPLICATIONUSED ONNEXT ASSYPROPRIETARY AND CONFIDENTIALTHE INFORMATION CONTAINED IN THISDRAWING IS THE SOLE PROPERTY OF<INSERT COMPANY NAME HERE>.  ANY REPRODUCTION IN PART OR AS A WHOLEWITHOUT THE WRITTEN PERMISSION OF<INSERT COMPANY NAME HERE> IS PROHIBITED.5 4 3 2 1Figure A.21: Drawing of outer shield ’s adapter.A.6 Electrical Feedthroughs and WiringAs can be seen in Figure A.27, there are three electrical feedthroughs in the cryo-stat:1. The original 10-pin electrical feedthrough of cryostat, which six of its pinswas used for the silicon diode and a thermal heater by the company. Weconnected four of its pins to four ”MWS” 36 AWG manganin wires. Eachline has a resistance of about 27 Ω.2. A circular 9-Pin, subminiature-C feedthrough on a 1.33 CF flange (part num-ber: 100010) with air and vacuum PEEK Polymer 9-Pin UHV Subminiature-C connectors (part number: 100040), which was made by ”Accu-Glass Prod-ucts Inc.”, was placed instead of a blank flange. All of its pins were con-nected to nine ”MWS” 36 AWG manganin wires. Each line has a resistanceof 18-19 Ω131Figure A.22: Photograph of gold-plated shield and its adapter.1323.8580.0890.118 0.1380.0270.1180.0394 clear holes for 2-56 screws1.9690.6300.0700.5510.2950.2360.07016 Threaded holes for 2-56 screwsDO NOT SCALE DRAWINGOuter ShieldSHEET 1 OF 1UNLESS OTHERWISE SPECIFIED:SCALE: 1:2 WEIGHT: REVDWG.  NO.ASIZETITLE:NAME DATECOMMENTS:Q.A.MFG APPR.ENG APPR.CHECKEDDRAWNFINISHMATERIALINTERPRET GEOMETRICTOLERANCING PER:DIMENSIONS ARE IN INCHESTOLERANCES:FRACTIONALANGULAR: MACH      BEND TWO PLACE DECIMAL    THREE PLACE DECIMAL  APPLICATIONUSED ONNEXT ASSYPROPRIETARY AND CONFIDENTIALTHE INFORMATION CONTAINED IN THISDRAWING IS THE SOLE PROPERTY OF<INSERT COMPANY NAME HERE>.  ANY REPRODUCTION IN PART OR AS A WHOLEWITHOUT THE WRITTEN PERMISSION OF<INSERT COMPANY NAME HERE> IS PROHIBITED.5 4 3 2 1Figure A.23: Drawing of 30 K outer shield.Figure A.24: Photograph of 30 K outer shield.1330.039 0.0390.2760.1570.0891.3000.1570.1970.2954 Clear Holes for 2-56 screwsTwo pieces needed.DO NOT SCALE DRAWINGslide add.SHEET 1 OF 1UNLESS OTHERWISE SPECIFIED:SCALE: 2:1 WEIGHT: REVDWG.  NO.ASIZETITLE:NAME DATECOMMENTS:Q.A.MFG APPR.ENG APPR.CHECKEDDRAWNFINISHMATERIALINTERPRET GEOMETRICTOLERANCING PER:DIMENSIONS ARE IN INCHESTOLERANCES:FRACTIONALANGULAR: MACH      BEND TWO PLACE DECIMAL    THREE PLACE DECIMAL  APPLICATIONUSED ONNEXT ASSYPROPRIETARY AND CONFIDENTIALTHE INFORMATION CONTAINED IN THISDRAWING IS THE SOLE PROPERTY OF<INSERT COMPANY NAME HERE>.  ANY REPRODUCTION IN PART OR AS A WHOLEWITHOUT THE WRITTEN PERMISSION OF<INSERT COMPANY NAME HERE> IS PROHIBITED.5 4 3 2 1Figure A.25: Drawing of additional slide part for outer shield.Figure A.26: Photograph of outer shield, shutter and its additional parts.134Figure A.27: Photograph of cryostat and its feedthroughs.3. A 4-pin power feedthrough, (5 KV, 25 AMPS) with 0.050” copper conductoron a 1.33 CF Flange (Item code: A0270-3-CF), which was made by ”MPFProducts Inc.”, was added to the system using a tee. Two of its pins wereagain connected to two ”MWS” 36 AWG manganin wires with the resistanceof 27 Ω. The two other pins in this feedthrough were used for magnet leadsand two 22 AWG kapton insulated silver plated copper wires from ”Accu-Glass Products Inc.” (part number: 100680) were connected to them.Since all of the wires were placed underneath the factory-made 30 K shield,the shield was removed first and then masterbond epoxy was used for gluing wiresto the stainless steel body as can be seen in Figure A.28 and Figure A.30. InFigure A.28, the extended wires on the tissue are the original wires that were in-stalled by factory for silicon diode temperature sensor and heater on the cold finger.We extended them by adding manganin wires to their ends. The circular 9-Pin,subminiature-C feedthrough can be seen in the corner of the photograph. Finally135Figure A.28: Photograph of manganin wires glued by masterbond epoxy tothe staniless steel body of can be seen in Figure A.29, the wires covered by ECCOSORB CR-124 epoxy.ECCOSORB CR-124 epoxy is a UHV compatible epoxy for attenuation in the fre-quency range of 1-18 GHz [See Figure A.30 and Table 3.1]. We will describe whywe need to use ECCOSORB epoxy for removing Johnson noise in the next section.A.7 Filtering Johnson Noise in WiringIn the experiments designed for detecting superconductivity, the main contributionto the noise is Johnson noise, which can be thought of as black body radiation thatcan propagate down the sample wiring. While detecting superconductivity was notthe main goal of this thesis, since superconductivity was probed at Chapter 7, webriefly discuss it here. At high frequencies, all wires can be thought of as havinga few hundred ohms of resistance–this value comes from the impedance of freespace, which is about 377 Ω. The noise is coming from the wires in the sense thatthe hot part of the wires generates voltage noise which propagates down throughto the cold part. It it known that for a given bandwidth, the root mean square(rms) of the voltage noise for a resistor, R, is given by√4kBTR∆ f , where T is the136Figure A.29: Photograph of manganin wires covered by ECCOSORB CR-124 epoxy.137Figure A.30: Photograph of black ECCOSORB and white masterbond epoxy.temperature of resistor and ∆f is the bandwidth in Hertz over which the noise ismeasured [189, 190].If we consider wires with a few hundred ohms of impedance–the same orderof magnitude as 377 ohms, then Johnson noise is estimated around 2.5 nV/√Hz atroom temperature. This noise is irrelevant to our lock-in amplifier measurements,because these measurements are only sensitive to noise within a small bandwidth(inverse of time constant of lock-in amplifier) around our operating frequency.However, the device sees all of the Johnson noise, integrated up to the highest fre-quencies that can propagate down our wires (>10 GHz for short, unfiltered wires).Assuming that frequencies up to 40 GHz can propagate down our wires, and thevoltage noise of 2.5 nV/√Hz, the full integrated noise across our device is 500 µV,or 0.5 µA across 1000 Ω of device.The relation between critical current (Ic) and superconducting energy gap (∆)at T = 0 K may be written as [191, 192]: IcRn = α∆/e where Rn is the normal stateresistance of the sample and α is a unitless number between 1 and 1/10 for mostof superconductors 1. For superconductivity in graphene, the theoretical value forα is predicted between 1 and 3 [192, 195]. However, there are some experimentalreports that have found α a factor of 20 smaller than predicted values [195].If we are looking for detecting a superconducting gap of 6 K (i.e. 500 µeV),then IcRn will be somewhere above 50 µV. Considering the normal resistance of a1The original relation for the full temperature dependence of IC in a Josephson tunnel junctionwas derived by Ambegaokar and Baratoff as: IcRn = (pi∆/2e)tanh(∆/2kBT ) [191, 193, 194]138graphene sample is around 1 kΩ, the critical current would be around 50 nA. So wecan see that our predicted noise current of 500 nA significantly exceeds the criticalcurrent.In order to solve this problem, our noise current needs to be dramatically de-creased by placing filters in the cold places. The primary concern for detectingsuperconductivity is black body radiation, not RF from microwaves or cell phonetowers, so if we place the filters outside the chamber they will not be effective. Forthese reasons, we decided to use RC filters placed on the cold finger [See Figure 3.5and Figure 3.15] between wires coming from the feedthrough and wires going tothe sample, as well as ECCOSORB CR-124 epoxy covering cold wires attachedto the body of cryostat underneath the 30 K shield [See Figure 3.14] and betweenthe RC filters and bottom connector. ECCOSORB CR-124 is a UHV compatibleepoxy for attenuation in the range of 1-18 GHz [See Table 3.1]. Further detailsabout wiring can be found in Section 3.11.A.8 RC FiltersA printed circuit board (PCB) with resistor-capacitor (RC) low pass filters is placedon the cold finger between the ECCOSORB covered wires, which enter and leaveit [See Figure 3.5]. The design is three RC filters in series for each wire: 332ohms+ 10nF + 332ohms + 1nF + 332ohms + 1nF (9×3=27 filters in total). For compact-ness and frequency response, these filters were made using surface mount compo-nents on a 17×18 mm2 FR-4 PCB [See Figure A.31]. Considering parasitic ca-pacitors and inductors, the response of these filters were simulated by “AdvancedDesign System” (ADS) software [See Figure A.32]. Figure A.33 shows the re-sults. In addition to the simulation, the real response of the circuit measured usingan “Anritsu MS2034A VNA Master” spectrum analyzer while sending signal by an“Agilent 83752A Synthesized Sweeper”. Table A.1 shows the measured responseat different frequencies. The RC filter boards were later glued to the cold fingerusing silver epoxy [See Figure 3.15 and Figure A.36] and covered by a shield madeof copper foil to protect from radiation pickup [See Figure A.37].139Figure A.31: Photograph of RC filters on PCB.voutLL1_ParasiticR=L=1 nHRR4R=50 OhmLL2_ParasiticR=L=0.8 nHLL3_ParasiticR=L=0.8 nHACAC1Step=0.01 MHzStop=50.0 GHzStart=1.0 kHzACCC3C=1 nFCC2C=1 nFCC1C=10 nFCC6_ParasiticC=25 fFCC5_ParasiticC=25 fFRR1R=332 OhmV_ACSRC1Freq=freqVac=polar(1,0) VCC7_ParasiticC=50 fFRR3R=332 OhmRR2R=332 OhmFigure A.32: The simulated RC filters circuit.140Figure A.33: The voltage response of the simulated RC filters. The red dotsshows the measured response of RC filters from Table A.1.Table A.1: The measured response of RC filters. The second and thirdcolumns are peak-to-peak input and output voltages. The last columnis output to input voltage ratio.Frequency VInput (V) VOut put (V)VOut putVInput(dBV)9 kHz 1.190 1.140 -0.3710 kHz 1.180 1.130 -0.3850 kHz 1.000 0.650 -3.74100 kHz 1.000 0.360 -8.87200 kHz 1.000 0.168 -15.49300 kHz 1.000 0.080 -21.94400 kHz 1.000 0.017 -35.39500 kHz 1.000 0.010 -40.001 MHz 1.000 0.007 -43.1010 MHz 1.000 Nothing Observable500 MHz 1.000 Nothing Observable141A.9 AssemblingAfter wiring, we started to assemble and install different parts. First, the 30 Kgold-plated shield, the 4.62” to 2.75” CF neck adapter, 8” CF and finally the outershield adapter was placed using their screws and bolts [See Figure A.34]. Second,the magnet frame glued by copper paste (TR-890 M from ”Tanaka Kikinzoku In-ternational K.K.”) and screwed to the cold finger of cryostat [See Figure A.35].In the next step, RC filters’ PCB glued to the magnet frame by silver epoxy andthe nine manganin wires coming from underneath the gold-plated shield were sol-dered to one side of filters [See Figure A.36]. Then, the bottom connector andthree copper alignment rods was placed inside and screwed to the magnet frameand its ECCOSORB covered nine manganin wires coming from female pins weresoldered to the end of RC filters [See Figure A.20 and Figure A.36]. Then, RCfilters were covered by two copper shields[See Figure A.37]. As can be seen inFigure A.38, soldering copper wires coming from magnet to HTS wires was doneafterwards.A.10 Measuring Magnet’s Field to Current ratioA linear Hall effect sensor IC (A1324) was used to measure the magnetic field thatcan be produced by applying a special current. This sensor and a 0.1 µF capacitorwas glued on a silicon substrate and made a circuit as shown in Figure A.39. Then,this silicon substrate was put in the sample holder and the sample holder was placedinside the magnet frame. When Vcc = 5 V, the sensor has a sensitivity of 5 mV/-Gauss (i.e. 20 mT/V). The Table A.2 and Figure A.40 show the sensors output volt-age in different currents, which was applied to the custom-made superconductingmagnet. The magnetic field to current ratio (B/I) is the slope in Figure A.40 mul-tiply by Hall sensor’s sensitivity. Therefore, B/I = 0.9(V/A)× 20(mT/V ) = 18mT/A. This measured ratio is close to our rough estimation. We can roughly con-sider our magnet as a solenoid with a inner diameter of din = 2.5 cm, outside diam-eter of dout = 4.3 cm, number of turns of N = 465, and length of l = 0.8 cm, thenB/I = µ0N(√d2out + l2+d2out)/((√d2in+ l2+d2in)(dout −din)) = 17 mT/A.142Figure A.34: Placing gold-plated shield and 8” CF.143Figure A.35: Gluing and screwing magnet frame to the cryostat’s cold finger.144Figure A.36: Gluing and screwing bottom connector to the magnet frame.The glued RC filters PCB can also be seen in these photographs.145Figure A.37: Photograph of RC filters copper shields.146Figure A.38: Photograph of copper wires coming from magnet soldered toHTS wires.147Figure A.39: Circuit map for sensing magnetic field.Table A.2: The output voltage of Hall sensor versus magnet’s applied current.Vapp (V) Iapp (A) Vout (V)0 2.4932 0.1 2.3980.2 2.3090.3 2.2200.4 2.13610 0.5 2.0410.6 1.9540.7 1.8580.8 1.7680.9 1.68121.1 1.0 1.5931482. out (V) (A)Vout=-0.900 Iapp+2.491Figure A.40: The output voltage of Hall sensor versus magnet’s applied cur-rent.A.11 Placing Removable Parts: Sample Holder, CoverPlate, Outer Shield, and ShutterIn the section Section A.9, assembling permanent parts of setup was described. Inthis section, we will talk about placing removable parts like sample holder, coverplate, outer shield and shutter which every time that the sample need to be changed,will be removed and placed back latter when a new sample goes in. For the firsttime for testing the temperature more accurately, instead of a graphene sample, acalibrated Allen Bradley resistor glued to an un-doped silicon substrate by H77epoxy, was pasted to the bottom of sample holder by silver paint. Later, insteadof silver paint, samples were always glued by a UHV compatible high temperaturetolerant copper paste (TR-890 M from ”Tanaka Kikinzoku International K.K.”)and H20 silver epoxy was used for connecting wires from samples to the pins.In the case of Allen Bradley resistor, four wires from Allen Bradley resistor wereconnected to four pins (two wires at each side of Allen Bradley) by H20 silverepoxy. Finally after putting sample, sample holder can be plugged into the magnetframe [See Figure A.41]. The three copper alignment rods help to plug all of nine149male pins of sample holder to the nine female counter pins of bottom connector.After plugging sample holder, the cover plate was placed and screwed to bottomconnector. In fact, both cover plate and sample holder were connecting thermallyto the bottom connector with these 4-40 titanium screws [See Figure A.42]. Thecombination of cover plate and magnet frame made a 4 K shield for the sample witha hole in the center of cover plate for the purpose of letting evaporated adatoms’reach the graphene sample. Placing outer shield as a continuation of 30 K shieldwas the next step. The outer shield were connected to the adapter and the goldplate shield by four 2-56 titanium screws [See Figure A.43]. The last step wasplacing shutter and the stainless steel rod which connect shutter to the wobble stickand let us move shutter inside vacuum with moving the wobble stick in air [SeeFigure A.44]. After placing all of these parts, the 8” conflat flange was put on topof UHV chamber [See Figure 3.17].A.12 ThermometeryAs mentioned before, the temperature of the cryostat cold finger can be monitoredwith a silicon diode (Lakeshore DT-670B-SD) installed by the factory [See Fig-ure 3.5].For the first cooldown, a calibrated Allen Bradley resistor loaded in the placeof the sample [See Figure A.41 for its picture and Table A.3 for its calibration].The Allen Bradley resistor is a carbon resistors, which is widely used as secondarythermometers at low temperatures. They are very sensitive, with little dependencyon magnetic field, and stable enough for a 10 mK precision. Our measurement ofthe Allen Bradley resistance in the first cooldown showed that there is no notice-able temperature difference between the sample holder and the cryostat cold fingerdown to 4.4 K [See Figure A.45]. We also checked whether running the super-conducting magnet causes any warming. Up to 5 A (i.e. 90 mT) no detectablewarming was observed. At 6 A (i.e. 108 mT), a small increase of 15 mK on theAllen Bradley was observed, while no change detected in the silicon diode.Later for measuring temperature of graphene sample more accurately, a CernoxTMresistance sensor (CX-1050-BG-HT) with a small copper foil shield was attachedto the wall of sample holder with H77 epoxy to check the temperature of sample di-150Figure A.41: Plugging the sample holder with an Allen Bradley in place ofsample. The tip of three copper alignment rods can be seen in thepicture.rectly [See Figure 3.5]. In addition to these thermometers, cryogenic temperaturesin the graphene were monitored via the electron-electron contribution to resistiv-ity and weak localization measurements, as will be explained in Section 7.2. Thetemperature sensed by Cernox and silicon diode was the same except in time ofadatom deposition. The sample temperature rose by at most 1 K during evapora-tion. Warming of sample during magnetic field sweep is also checked by Cernox[See Figure A.46].151Figure A.42: Mounting the cover plate over sample holder and screwing bothto the bottom connector.152Figure A.43: Mounting the outer shield.153Figure A.44: Installing shutter and its rod for connection to wobble stick.154Table A.3: Our Allen Bradly resistor calibration table.Temperature (K) Resistance (Ω)1.95 54152 51503 18503.5 13504 10605 73410 33720 21040 154.560 136100.3 119.1150 109.4200 106.1250 104.4300 104.5Figure A.45: The resistance of Allen Bradley resistor (RAB) vs. silicon diodevoltage (mV) during first cooldown from 77 K to 4.4 K.155Figure A.46: The temperature of sample measured by Cernox resistor duringthree magnetic field sweep in the range of (-100 mT, 100 mT).A.13 Other Parts of UHV ChamberOur UHV chamber consists of six 8” conflat flanges. As we mentioned before, allof the parts that mentioned till Section A.11 placed on the top 8” conflat flange andthe evaporator was on the bottom 8” conflat flange in the UHV chamber. One ofthe other side flanges is a window [See Figure A.47]. The flange on the other sideof window flange is connected to a residual gas analyser. One of other side flangesis connected to ”TMH521 P N Pfeiffer Turbomolecular Drag Pumps”, which it-self has another turbomolecular pump (”Pfeiffer TCP 120”) and a dry rough pump(”nXDS scroll pump”) as its backup. The remaining flange is connected to a tita-nium sublimation pump (TSP) and a crystal monitor. It also possible to substituteTSP with a UHV variable leak valve.A.14 Resistance MeasurementsSince DC measurements are susceptible to errors from thermoelectric voltage off-sets and the high noise of amplifiers at low frequency, we applied an AC bias, andmeasured the resulting AC output. This means the input and output values wediscuss are actually root mean square (rms) values.156Figure A.47: Photograph of window flange in the UHV chamber. Part ofouter shield, crystal monitor and old evaporation source box can beseen in this photograph.To generate the AC bias and to measure the rms amplitude, an SR830 lock-inamplifier and QSIT voltage amplifiers was used. The chosen AC frequency was inthe range 70 Hz to 100 Hz (often 83 Hz), the value depending on what frequencythat, at the time, was least influenced by interference. The lockin was set up with atime constant of 100 ms, on the 24 dB/oct filter slope setting. The current bias was100 nA in most of measurements. This bias was produced with sending an 0.1 Vlockin output through 1 MΩ resistor. However, current biases of 10 nA and 1 nAwere occasionally used.157Appendix BMobility and Diffusion Constantof Unannealed SamplesMeasurements of this appendix were performed on four different graphene devices:three epitaxial graphene samples on SiC (SiC1-3), and one samples grown by CVDand transferred on to SiO2/Si chips (CVD1). Further details about the samples areprovided in Section 4.1.As can be seen in Figure B.1 (a) and (b), the inverse mobility and diffusionconstant of unannealed SiC1,2,3 do not follow the long-range theory. Using theirslopes of 1/µ versus ∆n, we foundC= 4−6×1016 V−1.s−1, which is higher thanpredicted value and probably is a sign of Li adatom clustering. The effect of Liadatoms on sample diffusion constant is drastically reduced before, compared to,after annealing, consistent with the doping effects described in Chapter 5. Withoutannealing, the diffusion constant of SiC1,2,3 did not change due to Li, and in caseof SiC3 remained about 268.8 cm2/s [Figure B.1 (b)]. But after annealing at 900K, the diffusion constant decreased by over a factor of 6, from 206.5 cm2/s to 32.7cm2/s for SiC3 [Figure 6.5 (b)].The reason for inconsistency with long-range theory in Figure B.1 is the factthat most of data points are in saturation region. Figure B.2 shows data for CVD1that were taken mostly before saturation. Assuming charge transfer of η = 0.6−0.7, the slope in Figure B.2 results in C = 20e/h ≈ 5× 1015 V−1.s−1 which isconsistent with what is predicted for long-range scattering in graphene on SiO2158280240200160D (cm2 /s)∆n (x1013 e-/cm2)(b)20161281/µ(V s/m2 )SiC1SiC2SiC3(a)Figure B.1: (a) The inverse mobility and (b) diffusion constant versus changeof charge carrier density induced by Li deposition for of the SiC1,2,3.100806040201/µ (V s/m2)250200150100500∆n (x1015 e-/m2) CVD1-1st run CVD1-2nd runFigure B.2: The inverse mobility versus change of charge carrier density in-duced by Li deposition for of the CVD1.159substrate 1 [19].1For η = 0.9, C still has the same order of magnitude and would be C = 3×1015 V−1.s−1.160


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