Science, Faculty of
Physics and Astronomy, Department of
DSpace
UBCV
Warner, Ashley Nicole
Master of Science - MSc
University of British Columbia
Topological materials are a newly discovered class of matter where protected gapless states arise within the material band structure. Of these materials is PtSn₄, a topological semimetal with experimentally confirmed Dirac nodal arcs in its band structure. It exhibits extremely large magnetoresistance and a high residual resistivity ratio which is indicative of efficient electron transport. There are many material characteristics responsible for excellent carrier mobility such as a topological surface state or low density defects to name a few. Since materials can exhibit high mobility without being topological, it is unknown how much of the assumed high mobility of PtSn₄ is dependent on its topological features versus something else entirely. Scanning tunneling microscopy and spectroscopy is a surface sensitive technique that allows for the imaging of a conductive surface at an atomic resolution via quantum tunneling. It is an excellent tool for studying imperfect crystal lattices due to defects, characterizing cleaving terraces of materials and probing both occupied and unoccupied electron states. In this thesis, scanning tunneling microscopy and spectroscopy is used to explore PtSn₄ in detail. The structure of the pristine lattice is defined and the three different possible terrace steps are identified using differing spectroscopies as well as comparing terrace step edge heights to distances within the unit cell. One of the main goals was to explore the intrinsic defect density of the material and provide clarity to the cause of the high residual resistivity ratio. Five different types of defects are documented in both topographic and spectroscopic detail. The lattice site origins of each defect is discussed in hopes to provide a strong basis for future exploration.
Defect and Terrace Characterization of PtSn4 usingScanning Tunneling Microscopy and SpectroscopybyAshley Nicole WarnerB.Sc., UC San Diego, 2018A THESIS SUBMITTED IN PARTIAL FULFILLMENTOF THE REQUIREMENTS FOR THE DEGREE OFMaster of ScienceinTHE FACULTY OF GRADUATE AND POSTDOCTORALSTUDIES(Physics)The University of British Columbia(Vancouver)July 2022© Ashley Nicole Warner, 2022The following individuals certify that they have read, and recommend to the Fac-ulty of Graduate and Postdoctoral Studies for acceptance, the thesis entitled:Defect and Terrace Characterization of PtSn4 using Scanning Tunnel-ing Microscopy and Spectroscopysubmitted by Ashley Nicole Warner in partial fulfillment of the requirements forthe degree of Master of Science in Physics.Examining Committee:Douglas Bonn, Professor, Physics and Astronomy, UBCSupervisorSarah Burke, Professor, Physics and Astronomy, UBCSupervisory Committee MemberAlannah Hallas, Professor, Physics and Astronomy, UBCSupervisory Committee MemberiiAbstractTopological materials are a newly discovered class of matter where protected gap-less states arise within the material band structure. Of these materials is PtSn4, atopological semimetal with experimentally confirmed Dirac nodal arcs in its bandstructure. It exhibits extremely large magnetoresistance and a high residual resis-tivity ratio which is indicative of efficient electron transport. There are many mate-rial characteristics responsible for excellent carrier mobility such as a topologicalsurface state or low density defects to name a few. Since materials can exhibit highmobility without being topological, it is unknown how much of the assumed highmobility of PtSn4 is dependent on its topological features versus something elseentirely.Scanning tunneling microscopy and spectroscopy is a surface sensitive tech-nique that allows for the imaging of a conductive surface at an atomic resolutionvia quantum tunneling. It is an excellent tool for studying imperfect crystal lat-tices due to defects, characterizing cleaving terraces of materials and probing bothoccupied and unoccupied electron states.In this thesis, scanning tunneling microscopy and spectroscopy is used to ex-plore PtSn4 in detail. The structure of the pristine lattice is defined and the threedifferent possible terrace steps are identified using differing spectroscopies as wellas comparing terrace step edge heights to distances within the unit cell. One of themain goals was to explore the intrinsic defect density of the material and provideclarity to the cause of the high residual resistivity ratio. Five different types ofdefects are documented in both topographic and spectroscopic detail. The latticesite origins of each defect is discussed in hopes to provide a strong basis for futureexploration.iiiLay SummaryPtSn4 is a type of material where the energy levels its electrons can occupy showinteresting properties. In addition, the surface of the material behaves completelyunlike the rest of the material. These types of materials have created a buzz in thescientific community in the last 15 years or so because they hold a lot of promise inquantum computing applications. Through preliminary testing, PtSn4 shows signsof a high crystal purity — implying electrons can flow easily with no defects block-ing their path. Scanning tunneling microscopy and spectroscopy allow researchersto view the surface of conducting materials at an atomic scale as well as probe theenergy levels the electrons are (or are not) occupying. This thesis documents acomprehensive exploration of characterizing PtSn4 and its impurities via scanningtunneling microscopy and spectroscopy.ivPrefaceThis thesis contains unpublished work and was written by me.The PtSn4 sample used in this thesis was grown by Samikshya Sahu under theguidance of Professor Alannah Hallas and the Hallas Lab at the Stewart-BlussonQuantum Matter Institute (SBQMI).The scanning tunneling microscopy and spectroscopy data in Chapter 3 andChapter 4 was collected by me as well as Dong Chen under the supervision ofProfessor Douglas Bonn and Professor Sarah Burke at the University of BritishColumbia in the Laboratory for Atomic Imaging Research at SBQMI. The majorityof data in Chapter 5 was taken by me with the rest by Dong Chen.All analysis in this work was completed by me. All STM images and lineprofiles were analyzed and processed using Gwyiddion [1]. Histogram data wasprocessed using WSxM [2]. The code used for spectra analysis was written by meor was code that belongs to the Laboratory for Atomic Imaging edited either solelyby me or with the help of Vanessa King.All figures in this work are original and authored by me with the exception ofFigure 1.4 which shows data from references [3] and [4].vTable of ContentsAbstract . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . iiiLay Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ivPreface . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . vTable of Contents . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . viList of Tables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ixList of Figures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xGlossary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xxviiAcknowledgments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .xxviiiDedication . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xxx1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11.1 Topological materials . . . . . . . . . . . . . . . . . . . . . . . . 11.2 Topological semi-metal PtSn4 . . . . . . . . . . . . . . . . . . . 41.2.1 The sample in this work . . . . . . . . . . . . . . . . . . 71.3 Goal of this thesis . . . . . . . . . . . . . . . . . . . . . . . . . . 81.4 Thesis overview . . . . . . . . . . . . . . . . . . . . . . . . . . . 92 Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 112.1 The history of the scanning tunneling microscope . . . . . . . . . 11vi2.2 The physics behind STM . . . . . . . . . . . . . . . . . . . . . . 112.3 The components of an STM . . . . . . . . . . . . . . . . . . . . 152.3.1 Key requirements . . . . . . . . . . . . . . . . . . . . . . 152.4 Topographic measurements . . . . . . . . . . . . . . . . . . . . . 202.4.1 Double and multi-tips . . . . . . . . . . . . . . . . . . . 212.5 Spectroscopic measurements . . . . . . . . . . . . . . . . . . . . 252.5.1 STM tunneling equation . . . . . . . . . . . . . . . . . . 262.5.2 Grid Maps . . . . . . . . . . . . . . . . . . . . . . . . . 282.6 Spectroscopic influence on topographic imaging . . . . . . . . . . 282.7 The STM in this work . . . . . . . . . . . . . . . . . . . . . . . . 323 Topography and spectra of pristine surfaces . . . . . . . . . . . . . 343.1 Pristine topography . . . . . . . . . . . . . . . . . . . . . . . . . 343.2 Pristine spectroscopy . . . . . . . . . . . . . . . . . . . . . . . . 383.3 Terrace characterization . . . . . . . . . . . . . . . . . . . . . . . 423.4 Final terrace determinations . . . . . . . . . . . . . . . . . . . . 504 Topography and Spectra of Defects . . . . . . . . . . . . . . . . . . 524.1 4-fold symmetry defect . . . . . . . . . . . . . . . . . . . . . . . 534.1.1 4-fold topography and spectroscopy . . . . . . . . . . . . 534.1.2 4-fold lattice overlay . . . . . . . . . . . . . . . . . . . . 564.2 Spearhead defect . . . . . . . . . . . . . . . . . . . . . . . . . . 574.2.1 Spearhead topography and spectroscopy . . . . . . . . . . 574.2.2 Spearhead lattice overlay . . . . . . . . . . . . . . . . . . 614.3 Crescent defect . . . . . . . . . . . . . . . . . . . . . . . . . . . 624.3.1 Crescent topography and spectroscopy . . . . . . . . . . . 624.3.2 Crescent lattice overlay . . . . . . . . . . . . . . . . . . . 634.4 Butterfly defect . . . . . . . . . . . . . . . . . . . . . . . . . . . 654.4.1 Butterfly topography and spectroscopy . . . . . . . . . . 664.4.2 Butterfly lattice overlay . . . . . . . . . . . . . . . . . . . 664.5 Croissant defect . . . . . . . . . . . . . . . . . . . . . . . . . . . 704.5.1 Croissant topography and spectroscopy . . . . . . . . . . 714.5.2 Croissant lattice overlay . . . . . . . . . . . . . . . . . . 73vii4.6 Recap of defects . . . . . . . . . . . . . . . . . . . . . . . . . . . 765 Analysis of rotating defects . . . . . . . . . . . . . . . . . . . . . . . 785.1 The Rotating Defect . . . . . . . . . . . . . . . . . . . . . . . . . 795.2 Peculiar related phenomena . . . . . . . . . . . . . . . . . . . . . 835.3 Proposed theory behind rotations . . . . . . . . . . . . . . . . . . 886 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 926.1 Future directions . . . . . . . . . . . . . . . . . . . . . . . . . . 94Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 96viiiList of TablesTable 3.1 A table showing approximate suggestions ofVbias depending onwhat surfaces are being scanned. These biases should minimizethe DOS influence between the corresponding terraces. . . . . 50Table 4.1 A table showing approximate suggestions ofVbias depending onwhat defects are being scanned. These biases should best showthe finer details of the defects as well as show the underlyingpristine crystal structure. It should be noted that although aVbiasaround +300 mV for the butterfly defect will show its specificdetailing, the best the atomic resolution will be very difficult toacquire at this bias. . . . . . . . . . . . . . . . . . . . . . . . 77ixList of FiguresFigure 1.1 (a) A matzo ball deforming into a towel. No holes or tearsare needed to create the shape of the towel. Therefore a matzoball and a towel have the same topology. (b) A bagel can bemorphed into a coffee mug as well as a fire hose. All three ofthese items have one hole permeating through its material. Theobjects in (a) are not topologically equivalent to the objects in(b). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2Figure 1.2 Four different diagrams of cartoon band structures that show-case the key properties of metals, insulators, semiconductorsand semi-metals respectively. The valence band is representedby the bottom orange downward facing parabolic curve. Theconduction band is shown by the top blue upward facing paraboliccurve. Solid circles represent occupied states, empty circlesrepresent unoccupied states and the dashed line cutting acrosshorizontally represents the Fermi energy. The electronic prop-erties of a material depend on which type of band (valence orconducting) houses the highest energy electron at the Fermienergy. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3Figure 1.3 (left) A graph of a fictional band structure as seen in Figure 1.2.(right) A plot showing the topology of the band structure fromthe left at the Fermi energy, often referred to as an energy slice. 3xFigure 1.4 (a) magnetoresistance (MR) Data on PtSn4 [4]. (b) ARPESdata of PtSn4 and (c) ARPES schematic of the band structureof PtSn4 showing Dirac nodal lines [3]. . . . . . . . . . . . . 4Figure 1.5 (a) A slanted side profile of a PtSn4 unit cell showing bondsto each atom’s nearest neighbors. This reveals a plane halfwaydown the unit cell in between two Sn layers that makes PtSn4a good candidate for cleaving. (b) An incident view of thesurface of the PtSn4 unit cell. . . . . . . . . . . . . . . . . . . 5Figure 1.6 Renderings of PtSn4 normal to the cleaving surface. (a) In-cident view of half of the unit cell along the b direction. (b)Incident view of the first two layers of the unit cell consist-ing of only Sn (top layer) and Pt (second layer). (c) First twolayers of Sn and Pt showing nearest neighbor bonds. . . . . . 5Figure 1.7 A side profile of PtSn4 denoting the labeling mechanism usedand often referred to throughout this work. The unit cell isvisually divided by Sn2a and Sn1b. This spacing holds promisefor a dependable cleavage plane. . . . . . . . . . . . . . . . . 7Figure 1.8 A side profile of PtSn4 with common spaces measured andlisted according to references [3, 4, 70]. The most probablecleaving plane occurs between Sn2a and Sn1b where no Ptlayer separates them. . . . . . . . . . . . . . . . . . . . . . . 8Figure 1.9 The PtSn4 sample scanned on in this work before cleaving.This sample was grown by the Hallas Lab at the Universityof British Columbia. Sample grown and photo taken by PhDstudent Samikshya Sahu. . . . . . . . . . . . . . . . . . . . . 9Figure 2.1 A set of cartoon images providing an analogy of classical me-chanics. (a) If the energy of the basketball is less than theenergy required to keep the brick wall together (ie, Tbasketball <Ubarrier, the basketball will not penetrate the brick wall. (b) IfTbasketball >Ubarrier, then the energy will go into destroying thebrick wall and the basketball will break through. . . . . . . . 12xiFigure 2.2 A set of images implying that basketballs are traveling throughtwo vertical slits in a brick wall (one can imagine many bas-ketballs being thrown incident onto the brick wall). (a) In thisclassical analogy, the basketballs on the correct trajectory canbe expected to travel through the slits and hit the backdrop ina way that mimics the shape of the slits as highlighted in blue.(b) If the basketballs behaved like quantum particles then upontraveling through two slots they would create a diffraction pat-tern on the backdrop, similar to how waves would. This re-sult isn’t seen of macrosized objects such as a basketball butis exactly how smaller objects function where quantum lawsdominate over classical ones. . . . . . . . . . . . . . . . . . . 13Figure 2.3 (top) Cartoon example of an electron tunneling through a bar-rier. (bottom) Analogous wave equation of the same transmis-sion phenomenon. In both cases the wave equation becomes adecaying exponential inside the barrier and resumes to oscilla-tory behavior past it. . . . . . . . . . . . . . . . . . . . . . . 14Figure 2.4 A diagram demonstrating how the tip moves across the surfaceof a material. Re f f is the internal resistance of the STM circuitand Vbias is the voltage set by the user. (a) The tip is scan-ning on a single terrace and the incoming current Iset = Io. (b)The tip approaches a new terrace, shortening the distance fromthe tip to the sample. This increases the live current, whereIset < Inew as well as the previous Io. This is because znew < zoas a result of the approaching terrace. (c) The feedback loop in-takes this new information and raises the tip in the zˆ direction,restoring the distance to zo thus setting the incoming currentback to Iset . This movement in the zˆ direction is recorded anddisplayed as a topographical map (diagram is not to scale). . . 17xiiFigure 2.5 (a) A picture of the tungsten (W) STM tip through a micro-scope taken June 17th, 2021, just before being inserted intothe STM. This tip was used to take a majority of the data de-scribed in this work. (b) The same tip after being used by theSTM for six months, taken mid December 2021. Even thoughthe tip in figure (b) is noticeably shorter and more blunt, it isstill possible to get one atom dominating the edge of the tip, al-lowing for atomic resolution. (c) A zoomed in representationof what the atomic surface of the tips in both (a) and (b) couldlook like on the surface. . . . . . . . . . . . . . . . . . . . . 19Figure 2.6 (a) A representation of the real surface the tip is scanning, botha defect (left) and a step edge (right). (b) A chart showingwhat different topography looks like based off of tip shape.The first row is data that is to be expected from a singular,atomically sharp tip, where one defect and one step edge iscorrectly shown in the second and third column respectively.In rows two, three, and four, the effects of a smaller secondtip, an identical second tip, and a blunt tip are shown. . . . . . 22Figure 2.7 Early scans of PtSn4 during tip preparation showcasing classicmulti-tip scans with (a) showing a double tip and (b) showingmultiple. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24Figure 2.8 A series of graphics that shows the DOS of the tip and an in-sulator for 3 different energy levels plotted vertically. (a) Arepresentation of a tunneling junction where the voltage biashas shifted EF of the tip to match EF of the sample. All elasticscattering processes align occupied/unoccupied states from thetip to occupied/unoccupied states to the sample respectively.Therefore no tunneling will occur. (b) A representation of atunneling junction where a positive bias is applied to the sam-ple allowing for electrons to tunnel from tip to sample. (c) Arepresentation of a tunneling junction where a negative bias isapplied to the sample. This reverses the flow of electrons andnow tunneling occurs from sample to tip. . . . . . . . . . . . 26xiiiFigure 2.9 A cartoon rendition of an imaginary material showing spec-troscopic influence on topographic data. (a) Arbitrary spectraof the two types of atoms. (b) A singular flat terrace with animagined domain boundary of atom B inside of an atom A do-main. As the tip scans across the flat terrace at Vbias = V1, thecurrent decreases in value, bringing the tip closer to the surfaceeven though the surface is flat and has no vertical topologicalvariations. (c) The resultant zˆ profile from the topographic scanof (b). Even though there is no true topographic variation, theinfluence of the DOS of the atom B domain can create a stepedge-like feature in the zˆ profile. . . . . . . . . . . . . . . . . 29Figure 2.10 A cartoon rendition of an imaginary material showing spectro-scopic influence on topographic data. (a) Arbitrary spectra ofthe two terraces discussed. α(ε) represents the gray dI/dVcurve of surface A while β (ε) the dark purple dI/dV curve ofsurface B. On the right, a terrace relaxation of δ A˚ is depicted.Values V1 and V2 are chosen where∫ V10 α(ε)dε >∫ V10 β (ε)dεand∫ V20 α(ε)dε =∫ V20 β (ε)dε . (b) Two diagrams showing vi-sual representations of the tip-to-sample distance h, scanningeach terrace atV1 andV2 respectively. Surface B has a lower in-tegrated density of states at V1 and therefore h is smaller com-pared to Surface A. At V2, the integrated DOS are equal. As aresult, h remains the same and there is no change in h betweensurfaces. (c) Resultant zˆ line profiles of diagrams in (b). The zˆprofile data with Vbias =V1 show an inflated value for the stepedge vertical distance due to the DOS influence. . . . . . . . . 31Figure 2.11 A picture of the STM used in this thesis. (top) A picture ofthe front of the STM. Pointed with arrows from left to right arethe manipulator arm, the prep chamber, the STM chamber, andthen above that is the cryostat. (bottom) A picture of the backof the STM. The load lock, its transfer arm, and the heliumrecovery line are labeled with arrows. . . . . . . . . . . . . . 33xivFigure 3.1 (a) An STM scan of a pristine surface of PtSn4 with no defects,taken at -350 mV and 600 pA. (b) Dotted lines overlayed ontop of the first Sn and Pt layer of the unit cell. The dotteddiagonal orange and straight blue lines correspond to the soliddiagonal orange and straight blue lines in part (a) respectively.(c) and (d) Height profiles of the topography along the blueand orange lines in figure (a) and (b). . . . . . . . . . . . . . 35Figure 3.2 An overlay of the first two layers of the PtSn4 unit cell (Sn1aand Pta) according to the lattice constants from [4, 70]. TheSTM image was scanned at -400 mV and 600 pA and thenunderwent a 2D FFT filter. The Pt atoms align along the darkerordered spots of the image, suggesting the darker spots of thewaffle pattern seen are the holes in the Sn surface where the Ptatoms rest underneath. The blue and orange lines represent theline profiles taken on the 2D FFT image giving the Pt distancesto be 6.22±0.05 A˚ and 4.43±0.03 A˚ respectively. . . . . . . 37Figure 3.3 A set of STM images of the same general area taken at variousVbias and all at Iset = 600 pA. From left to right, Vbias = -800mV, -400 mV, +370 mV, +600 mV, and +800 mV. One to twodefects are apparent on top of the surface. . . . . . . . . . . . 37Figure 3.4 (a) An STM scan of PtSn4 of a pristine surface with two mi-nor defects taken at -400 mV and 600 pA. (b) An STM scanof PtSn4 of a pristine surface with five minor defects takenat +300 mV and 600 pA. (bottom) The corresponding spec-troscopy measurements taken on the blue and orange dot re-spectively. The transparent vertical blue lines denote core spec-troscopic features that vary minimally — if at all — due to tipshape. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39xvFigure 3.5 (left) An STM scan of PtSn4 of a pristine surface with two mi-nor defects taken at +400 mV and 600 pA. (right) The corre-sponding spectroscopic measurement taken on the orange dot.The transparent blue lines denote the voltage placement of fea-tures consistently seen in the pristine base spectrum on thissurface. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40Figure 3.6 (a) An STM scan of PtSn4 of multiple terrace steps taken at+400 mV and 600 pA. (b) The corresponding spectroscopicmeasurements. The orange dot denotes the spectra taken onterrace A, the blue dot on terrace C. Note the vast differencesin shape, implying these two surfaces are not of the same ter-mination type. . . . . . . . . . . . . . . . . . . . . . . . . . . 40Figure 3.7 (a) An STM scan of PtSn4 of multiple terrace steps taken at+1.00 V and 600 pA. (b) The corresponding spectroscopy mea-surements. One taken on terrace G, H, and J. The H terrace hastwo spectroscopy measurements, one on top of the white dots(the left most purple dot) and one not (the right most blue dot).(c) An STM scan of different terraces taken at a later date takenat -400 mV and 600 pA. (d) The spectroscopy data correlatingto the dots on the respective terraces in part (c). . . . . . . . . 41Figure 3.8 A composite image of two separate scans showing a cascadeof eight different terraces in PtSn4. Both of these scans weretaken with a Vbias =−400mV and Iset = 600pA. . . . . . . . . 43Figure 3.9 (a) An STM image of multiple step edges of PtSn4 with twolines cut perpendicularly across said step edges to denote whereline profile data was sampled. The longer line cut is blue andcorresponds to (b) while the shorter one is orange and corre-sponds to (c). (b) and (c) have two step edge sizes listed at eachassociated step. The first size is the raw data, and the second isthe data after the 0.85 calibration factor was applied. . . . . . 44xviFigure 3.10 A histogram of the z profile of the corresponding STM imagematched with the vertical crystal lattice structure of PtSn4. Onthe right, the raw height profiles are shown as well as the cor-rected height profiles due to the assumed 0.85 calibration. Thisfigure shows that while the Sn1 is the more common termina-tion plane, a Sn2 termination is possible and also undergoes arelaxation. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45Figure 3.11 A segment of the spectra taken on the surface shown in Fig-ure 3.6 from +100 mV to +500 mV. The STM image wasscanned with a Vbias = +400 mV as denoted with a verticaldouble arrow. The LDOS at this particular bias varies quite abit for the two terraces, with terrace C having the lower LDOSof the two. . . . . . . . . . . . . . . . . . . . . . . . . . . . 47Figure 3.12 Two histograms of STM scans with step edges. The distancesbetween histogram peaks have been multiplied by 0.85 for theproper calibration. Scan (b) is a zoomed in scan of the dottedterrace in scan (a). The Sn2 terrace has an upwards directionalshift in (b) due to the DOS influence effect. The H terraceremains inconclusive as denoted by the two dashed lines in thehistogram in part (a). . . . . . . . . . . . . . . . . . . . . . . 48Figure 3.13 A histogram of the z profile of the corresponding STM imagematched with the vertical crystal lattice structure of PtSn4. Thez profiles in the histogram have been multiplied by 0.85 to ad-just for the calibration. The Pt lattice is seen relaxing downwards. 49Figure 3.14 The three different types of spectra found on the three separateterraces plotted against each other. The orange medium sizecurve is from the Sn1 surface, the small blue curve denotes Pt,and the larger dark purple curve is Sn2. . . . . . . . . . . . . 51Figure 3.15 The three different types of spectra found on the three separateterraces plotted on a log scale from a voltage range from -400mV to +850 mV. No voltage value permits all terraces to havethe same integrated DOS which would negate the DOS influence. 51xviiFigure 4.1 (a) The first recorded instance of the 4-fold defect. (b, d-f) Thesecond recorded instance of the 4-fold defect shown at multi-ple voltage biases. There was a month and a half of time inbetween these two occurrences, and tip shapes were drasticallydifferent at the two times. (c) Spectra taken on the center of the4-fold defect plotted against the pristine background, with thedifference between the two curves in black. . . . . . . . . . . 54Figure 4.2 Spectra on the four bright lobes of this defect plotted againstthe defect center and pristine spectrum. The first valley of thecenter and bottom lobe (around +500 mV) appears flattenedcompared to the other lobes as well as the pristine. No notableshifts are detectable, and the spectra closely resembles the Sn1terrace spectrum. . . . . . . . . . . . . . . . . . . . . . . . . 55Figure 4.3 Spectra ranged from -1.0 V to 0 V pulled from the grid mapof the 4-fold defect plotted on a log plot. The log plot revealsno obvious features in the negative energy region. The dI/dVcurve from the center of the defect crosses over the pristinespectrum at approximately -550 mV. . . . . . . . . . . . . . . 55Figure 4.4 A line profile of the recorded z height taken vertically acrossthe 4-fold defect. The depth of the center of the defect relativeto the surface is approximately 12 pm. The recorded z profileof the peaks above and below the defect is about 6 pm. . . . . 56Figure 4.5 An image of the 4-fold defect with an overlay of the first twolayers of this scan’s termination. Using what is known fromthe croissant defect detailed later in this chapter as well as theguide of the darker spots of the image, the overlay suggests aPt atom is expected to rest in the center of the 4-fold defect. . 56xviiiFigure 4.6 Various topographic STM scans of the spearhead defect at dif-ferent Vbias. (a), (b) Scans with Vbias = +1.0 V and +400 mVrespectively showing the three spearhead defects in the topright corner with two butterfly defects in the bottom half ofthe photo. (c), (d) Cropped images of (a) and (b). (e) Scan ofdefects at Vbias = -400 mV. At negative biases, the spearheaddefects appear as bright circles indicating a higher LDOS atthis negative range. At +400 mV the defects resemble spear-heads pointing downwards, and at +1.0 V appear darker andmore symmetrical. . . . . . . . . . . . . . . . . . . . . . . . 58Figure 4.7 Various spectroscopic measurements of the three spearheaddefects. (top left) STM scan of the surface the spectra wastaken on. (top right) the LDOS of the center of each defect.(bottom) The spectra of each center defect plotted with thepristine background. . . . . . . . . . . . . . . . . . . . . . . 59Figure 4.8 Plotted spectra from the center of a spearhead defect (dark pur-ple) as well as it’s two lobes (orange and blue) compared withthe pristine background shown in gray. In the positive biasrange the lobes are not suppressed. In the negative bias rangethe two lobes show a higher LDOS than both the center of thedefect and the pristine spectrum. . . . . . . . . . . . . . . . . 60Figure 4.9 (a) Linear plot of the spearhead center, spearhead lobe, and Ptterrace spectra. (b) Log plot of plot (a) taken from -500 mV to+500 mV. If any similar features exist in the Pt spectrum, noiseoverpowers them. . . . . . . . . . . . . . . . . . . . . . . . . 60Figure 4.10 A set of three paired STM images of the same spearhead de-fects taken at various biases. Second row is a replica of thefirst row except for a red circle around the Pt sites of interest.Columns (b) and (c) show the defects imaged at one bias over-layed with the Vbias =−400mV scan to better show the atomicresolution. (a) Pair of STM images of the spearhead defectwith a lattice overlay. (b) and (c) suggests a Pt atom resides atthe center of the defect for both +400mV and +1.0V . . . . . . 61xixFigure 4.11 Two scans of separate clusters of crescent defects. (left) Groupof crescent defects scanned at a voltage bias of -400 mV. (right)An STM scan of another cluster of crescent defects scanned at+400 mV. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62Figure 4.12 Two STM images of three crescent defects and an artifact inthe bottom center. (left) STM image of crescent defects takenat -400 mV in three different orientations. (right) Same STMimage of three crescent defects plus artifact taken at +800 mV. 63Figure 4.13 (a) STM scan of three crescent defects. (b) dI/dV curvesof the dark centers of each crescent versus the pristine back-ground taken from a grid map. The center of the crescent de-fects has ≈ ∆ 60 mV LDOS shift to the left of the first peak,while the other two higher magnitude peaks stay aligned withthe background. . . . . . . . . . . . . . . . . . . . . . . . . . 64Figure 4.14 (a) A linear plot of the bright and dark lobes of the defect com-pared with the Sn1 terrace background. The 60 mV shift isnoted by two vertical blue lines. (b) A log plot of the samespectra from 0 mV to 800 mV. The log plot clarifies the twohigher valued peaks do not undergo any energy shifts, as illu-minated by the orange vertical lines. . . . . . . . . . . . . . . 65Figure 4.15 STM photo measured atVbias = -400 mV of several crescent de-fects with an attempted overlay. The areas where the overlaysrefuse to align if a Sn placement is assumed are highlighted inred boxes. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 66xxFigure 4.16 STM photos taken at -400 mV with an attempted lattice over-lay assuming a Sn atom is the responsible site for the defectlocation. (a) STM scan showing the lattice overlay and (b)showing arrows to highlight the orientation discrepancy. Thethicker blue arrows slice down the defects center, starting fromthe proposed defect site and ending at the apex of the brightlobe. The thinner red arrows follow the proposed symmetry ofonly the lattice. In comparing the angles and order of the ar-rows of one defect to another, it is clear there is no consistencyin either. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67Figure 4.17 A set of STM images of the same two butterfly defects at arange of different Vbias and all at Iset = 600 pA. From left toright, Vbias = -370 mV, +270 mV, +300 mV, and +370 mV . . 67Figure 4.18 Two larger scans of the same area showing butterfly defects attwo separate biases. (left) 13 butterfly defects scanned at -370mV. At this negative bias they appear as bright ovals. (right)14 butterfly defects scanned at +350 mV (the scanning areawas shifted downwards to include a defect originally out offrame). At this positive bias they appear as dark soft squareswith a small bright dot appearing in the middle. At positive bi-ases (specifically +400 mV) the 90o orientation becomes easyto track. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 68Figure 4.19 Two scans of the same four butterfly defects, two pairs in dif-ferent orientations as well as an artifact at the bottom-right ofthe cluster. (left) STM scan at Vbias = -320 mV that has anoverlay of the Sn1 and Pt terraces on top of the image. (right)Same defects scanned at +320 mV showcasing the bright anddark lobes of the defect. This bias, although only 50 mV lowerthan the voltage bias used in the left scan of Figure 4.18, showsa much brighter center. . . . . . . . . . . . . . . . . . . . . . 68xxiFigure 4.20 (a STM scan at +320 mV of four butterfly defects spectroscopydata was extracted from. (b) dI/dV of the center of each but-terfly defects compared with the pristine surface. (c) dI/dVof each lobe of one butterfly defect compared to the pristinebackground. . . . . . . . . . . . . . . . . . . . . . . . . . . . 69Figure 4.21 Three photos of a lattice overlay on top of the butterfly defectat three separate biases. (a) Two butterfly defects with a latticeoverlay extended to cover each defect. The same Sn site fallson the same spot for both defects. (b) Lattice overlay on abutterfly defect aligned with the Pt spots in the background.The same Sn lattice site sits in the same area of the defect asproposed in scan (a). (c) Same lattice overlay placed on top ofa scan of the defect at a Vbias of +370 mV. . . . . . . . . . . . 70Figure 4.22 Three different STM images of the croissant defect. The firsttwo on the left were taken with aVbias = -400 mV while the lastone on the right at +800 mV. The two scans at the negative biasshow the defects taking a croissant like curvature shape whilethe ones in the positive bias assume a dark oblong shape. . . . 71Figure 4.23 (a) A pair of STM images of the croissant and butterfly de-fect taken at -400 mV and +400 mV from left to right. Thecroissants defects are circled. (b) A pair of STM images of thecroissant and butterfly defect taken at a different location andpoint in time compared to set (a) where Vbias = -400 mV and+400 mV respectively. . . . . . . . . . . . . . . . . . . . . . 72Figure 4.24 A larger topographic scan with Vbias = -400 mV illustratingseveral croissants (top right quadrant) as well as crescent de-fects (bottom right quadrant). An artifact can be seen in thelower left quadrant. . . . . . . . . . . . . . . . . . . . . . . . 72Figure 4.25 A large 50 nm2 image of many croissant defects taken towardsthe end of the experimental run scanned at Vbias = -400 mV. . 73xxiiFigure 4.26 An STM scan with about a dozen croissant defects. An over-lay of the first two PtSn4 unit cell layers are aligned with theatomic resolution seen in this scan to showcase the lattice place-ments the croissants have in common. The diamonds are ori-ented perpendicularly to the croissant, with the Sn atom at theacute angle of the diamond placed at the middle corner of thecroissant defect. . . . . . . . . . . . . . . . . . . . . . . . . . 74Figure 4.27 (a) Figure 4.26 with green circles around each croissant, not-ing matching lattice sites. (b) Same scan from (a) with thelattice overlay shifted up by one half unit cell and realigned tothe Pt in the scan. Circles are color coded to the different typesof lattice sites they aligned with. With this overlay, three dif-ferent lattice site options exist within one image, which is notconsistent with the defect presentation. (c) and (d) Two setsof the same STM image showing a close up of two croissantdefects with the correct and incorrect overlay respectively. . . 75Figure 4.28 A set of three STM images of croissants. Each croissant hasthe acute angle of the Sn layer sitting perpendicular inside it.The Sn atoms sitting in the acute angles of the diamonds arehighlighted with light hued circles. . . . . . . . . . . . . . . . 76Figure 5.1 Two consecutive STM scans of the same defects taken a fewminutes apart, showing that the top left and bottom right de-fects have moved via rotation. . . . . . . . . . . . . . . . . . 78Figure 5.2 A set of STM images read left to right with Vbias = −1.0Vand Iset = 600pA demonstrating the rotations of the croissantdefects. Each defect in every scan presented has a white outlineof the original positions of the defects to highlight the rotationsand travel during succeeding scans. . . . . . . . . . . . . . . 79xxiiiFigure 5.3 A series of four consecutive STM scans (read left to right) ofthe same scanning area and defects taken at a voltage bias of-1.0 V and Iset = 600 pA. Similar to Figure 5.2, the defects inthe first scan on the left are outlined in white. Said outline isoverlayed on additional scans to detail the movement of thecroissants. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 79Figure 5.4 Two consecutive scans of the same area showing both croissantand crescent defects. (left) STM image taken at -400 mV. Fivedefects are circled in orange. (right) The same five defects areoutlined in blue noting a rotation by 900 in either the clockwiseor counterclockwise direction. . . . . . . . . . . . . . . . . . 80Figure 5.5 A series of 15 STM images taken consecutively where eachcroissant defect rotates at least once. The first image was scannedwith aVbias = -400 mV while the other 14 were scanned at -1.0mV. All scans used an Iset = 600 pA. After the first scan at -400mV, each scan took 78.8 seconds to complete before the nextonce was immediately started. A white outline of the origi-nal defect locations is overlayed on each image to illustrate themovement. . . . . . . . . . . . . . . . . . . . . . . . . . . . 81Figure 5.6 A series of 9 STM images of the croissant defect. The first8 images were taken consecutively at Vbias = +800 mV with15.9 seconds in between each scan. The last scan was taken at-400 mV to better determine the angle of rotation. Elongateddefects as well as crisp lines cutting defects through the centersindicate rotations mid scan. . . . . . . . . . . . . . . . . . . . 82Figure 5.7 (a) A series of 6 STM scans taken over one defect, increasingthe magnitude of the negative Vbias by 100 mV each scan. Arotation was finally seen at -900 mV. (b) Consecutive scans 4.9s apart all using Vbias = -900 mV, showcasing rotations as wellas the third and fifth rotating mid scan. . . . . . . . . . . . . . 82Figure 5.8 A visual representation showing that rotations were not wit-nessed under |Vbias| = 690 mV. Values above |Vbias| = 1 Vcaused rotations, depicted by the ellipses on the line graph. . . 83xxivFigure 5.9 (a) Initial scan showing two croissants perpendicular to eachother within the orange circle. (b) Secondary scan showingthe bottom left defect of the highlighted pair had rotated by900. (c) The consecutive scan taken right after the tip tunneledat -1 V in the center of the image for 60 seconds. Circle showswhere the two defects were expected to be and are not. (in-sets) Zoomed in images of the croissant defects of interest. Allimages and stationary tip tunneling were scanned/performed atIset = 600 pA. . . . . . . . . . . . . . . . . . . . . . . . . . . 84Figure 5.10 The base figures of Figure 5.9 with all full croissant defectscounted and circled. (a) 26 defects are accounted for. (b) 26defects are accounted for after the one rotation from the de-fect of interest and some rotations of neighboring defects. (c)24 defects are accounted for showing that if the two defectsdid not “undefect” themselves, they must have traveled signif-icantly out of range. All scans had parameters of Vbias = -400mV and Iset = 600 pA. . . . . . . . . . . . . . . . . . . . . . 85Figure 5.11 Another instance where two croissant defects were recordedannihilating each other under the same experimental processdenoted in Figure 5.9. All scans had parameters ofVbias = -400mV and Iset = 600 pA. . . . . . . . . . . . . . . . . . . . . . 85Figure 5.12 A set of three consecutive STM images of several croissant de-fects. In between each scan the STM tip (while tunneling) waspurposefully moved over the bottom right defect in the direc-tion of the arrow in an attempt to influence rotation. (a) STMimage of four croissant defects where the tip moved a short dis-tance perpendicularly over the defect. (b) STM image showingthat three of the four defects rotated under the influence of thetip movement described in image (a). The technique was re-peated, dragging the tip now parallel to the defect. (c) Theconsecutive scan at the presumed safe -400 mV voltage bias,revealing two new defects shown in the circles. . . . . . . . . 86xxvFigure 5.13 A plot of four different spectra on or around a croissant defectwith insets of a small scan over a singular croissant and themysterious dot taken at Vbias = -400 mV. The brightest partof the defect is shown in orange and the dark area inside thedefect is shown in blue. The random dot is shown in darkpurple while the background is shown in gray. . . . . . . . . . 87Figure 5.14 Cartoon representations of a proposed theory behind the crois-sant rotations. (a) A demonstration of a vacancy underneath adislodged Sn atom shifting to the rightmost nearest neighbor,causing a rotation. (b) A demonstration of a vacancy-Sn pairshifting to the upper nearest neighbor causing a rotation. . . . 88Figure 5.15 A set of images displaying a lattice overlay and dislocated Snatoms. (a) the STM image used with a Vbias = -1.0 V and Iset =600 pA. (b) same image with the lattice overlay, showing theSn atoms that are “out of socket.” These are represented by thelarger light purple dots on the image. (c) the overlay of the firstSn and Pt layer without the STM image for clarity. . . . . . . 89Figure 5.16 (a) Close up of the STM image where two croissants appearedto merge and heal the lattice with an overlay of the Sn and Ptlayer, as well as showing the dislocated Sn defects. (b) Samescanning area after the defects disappeared, showing an unper-turbed crystal lattice overlay on top. . . . . . . . . . . . . . . 90xxviGlossary2D FFT 2D Fast Fourier TransformDFT density functional theoryDOS density of statesFFT Fast Fourier TransformFT-STS Fourier-transform scanning tunneling spectroscopyLDOS local density of statesMR magnetoresistanceQPI quasiparticle interferenceRRR residual resistance ratioSPM scanning probing microscopySTM scanning tunneling microscopySTS scanning tunneling spectroscopyUHV ultra high vacuumXMR extremely large magnetoresistancexxviiAcknowledgmentsFrom moving to a new country by myself, to a global pandemic, no one is moresurprised that I’m sitting here finishing this degree than me. In no way would I havebeen able to do it without the help and support from a few amazing individuals.First, I’d like to acknowledge and thank the people, who without them thisresearch project would not exist. I’d like to thank Dr. Alannah Hallas for providingus with the PtSn4 sample and for also lending a hand in a time of need to be mysecond reader. I’d also like to thank PhD student and friend, Samikshya Sahu, fordoing a wonderful job growing the sample and for being a joy to ask questions toand work with. PhD student Dong Chen deserves recognition as well, for withouthis tenacity for research this exploration of PtSn4 would not exist. Through all theups, downs and hiccups of STM and grad school, I enjoyed laughing and learningwith you and can’t wait to see where you take this project.A massive thank you to both of my advisors, Dr. Sarah Burke and Dr. DougBonn. Both of your constant compassion, understanding, advocacy and supporthelped me reach this finish line and allowed me to find a home in Canada. Specialthanks to Doug for your guidance and for patiently reading (and rereading) everybroken sentence and half-baked thought I forgot to finish while completing thiswork. Hopefully I fixed them all.I’d like to thank the whole LAIR group for the knowledge, support and fun.A special thanks to James for being a wonderful mentor to me during the rollercoaster that was the last few years of my life. Thank you Tim, Rysa and the rest ofthe hot choco-latte crew. I cherish your friendships.To the friends outside of LAIR, thank you for giving my heart a home. Frommy snowboarding buddies to my roommates (including the four legged one), thankxxviiiyou for being phenomenal humans.I’d like to thank the Garrett family for always adding an extra dinner plate forthis stranded American. Thank you for making me feel like I always belonged.To my family. Your unwavering support in all that I do means the world. Thankyou for believing in me and watching my research through Zoom even if it madezero sense. Special thanks to my mom, who applied for her first passport before Ieven accepted UBC’s offer, and who rushed to Vancouver as soon as the bordersallowed her.To my best friend and VFL, Bethany. From MSJC to UCSD to Canada. I amso so thankful for your insight, love and fervent loyalty.To Richard. Your kind heart and personality warms my soul. Your constantactions and words of comfort kept my head above water. Thank you for believingin me enough for the both of us.Lastly, and a bit un-traditionally, I’d like to thank 8-year-old Ashley, who neverstayed silent and never stopped asking questions.xxixThis one’s for me.Chapter 1IntroductionQuantum matter covers a wide breadth of materials where new properties and phe-nomena are being theorized and discovered every year [5–10]. These materialsare responsible for superconductors, organic electronic materials, skyrmions, Ma-jorana fermions, etc. All of these discoveries hold vast potential in technical ap-plications in high current devices, renewable energy, memristors for neuromorphiccomputing, and more [11–24].More research is being dedicated to exploring the unique topology quantummaterials exhibit [19, 21, 25–31]. In the last 20 years topological materials havebecome of great interest within the condensed matter community and hold massivepotential in today’s ever advancing technological market [7, 32–36].1.1 Topological materialsTopology is a mathematical field that studies the concept of invariance among theabstract deformation of various objects. Consider an artist attempting to make asculpture out of an initial solid lump of clay. The artist should be able to morphit into any shape she pleases. But if the artist creates even a singular gap or holesomewhere in the sculpture, say a handle, the sculpture is no longer topologicallyequivalent to its initial state, even though the material itself is the same. Thismorphing concept can be applied for all objects. For instance a matzo ball is topo-logically equivalent to a towel. It is also topologically equivalent to an empty can1of soda, a bowl, a pillow, a snowboard deck, and so on. A bagel on the other hand istopologically equivalent to a handled coffee mug and also an unplugged fire hose.But a matzo ball is not topologically equivalent to a bagel, and vice versa.Figure 1.1: (a) A matzo ball deforming into a towel. No holes or tears areneeded to create the shape of the towel. Therefore a matzo ball anda towel have the same topology. (b) A bagel can be morphed into acoffee mug as well as a fire hose. All three of these items have one holepermeating through its material. The objects in (a) are not topologicallyequivalent to the objects in (b).Scientists have begun to apply the mathematical ideas of topology to bandstructures of condensed matter physics. The band structure of a material can bedescribed by Bloch eigenfunctions which are found by taking advantage of thetranslational symmetry of a crystal lattice and solving Schro¨dinger’s equation fora periodic potential well. Bloch functions denote the energy for an electron at aspecific wave vector k for multiple solutions of the Schro¨dinger equation for theBrillouin zone, thus providing the band structure of the material [37–39]. A ma-terial’s band structure is the discrete dispersion of allowed energy states electronswithin said material can occupy. The arrangement and occupation of these bandsdictates whether a material is insulating, metallic, semi-metallic, or semiconduct-ing (depicted in Figure 1.2). The topology of the band structure refers to its shapewhen an energy slice is taken for a 2D k range, as shown in Figure 1.3.Topological insulators are a class of materials theorized around 2005 [40–42]and experimentally realized in 2006 for 2D topological insulators [43] and 20092Figure 1.2: Four different diagrams of cartoon band structures that show-case the key properties of metals, insulators, semiconductors and semi-metals respectively. The valence band is represented by the bottom or-ange downward facing parabolic curve. The conduction band is shownby the top blue upward facing parabolic curve. Solid circles repre-sent occupied states, empty circles represent unoccupied states and thedashed line cutting across horizontally represents the Fermi energy. Theelectronic properties of a material depend on which type of band (va-lence or conducting) houses the highest energy electron at the Fermienergy.Figure 1.3: (left) A graph of a fictional band structure as seen in Figure 1.2.(right) A plot showing the topology of the band structure from the leftat the Fermi energy, often referred to as an energy slice.for 3D [44, 45]. The materials are referred to as being topological due to traits ofthe band structure itself. While the bulk of the topological material remains in-sulating or semi-metallic/semiconducting (depending on the parent material), theband structure of the surface has distinct, well defined areas that “bridge” the gapbetween two topologically inequivalent states — whether that be from bulk to sur-face or surface to vacuum — suddenly creating a determinate “gapless” area of3the band structure where a band gap dominates [46, 47]. These topological statesare protected by time-reversal symmetry implying that scattering events should besuppressed, if present at all [35, 47–49]. The suppression of scattering events formaterials that are by definition surface sensitive makes them exciting candidates forscanning tunneling microscopy (STM) and scanning tunneling spectroscopy (STS)[48, 50–55].Figure 1.4: (a) magnetoresistance (MR) Data on PtSn4 [4]. (b) ARPES dataof PtSn4 and (c) ARPES schematic of the band structure of PtSn4 show-ing Dirac nodal lines [3].1.2 Topological semi-metal PtSn4PtSn4 is a topological semi-metal with extremely large magnetoresistance (XMR)[4, 56, 57] which is a strong indicator of potentially unique topological surfacestates [4, 56, 58–69]. PtSn4 is the first experimentally confirmed material to havea Dirac nodal arc in the band structure [3] which is protected by its crystallinesymmetry [57]. The interesting topological surface states, crystal structure, as wellas XMR makes PtSn4 a prime candidate to explore via STM.PtSn4 has an orthorhombic crystal lattice structure in the translationengleichecentrosymmetric Ccca (No. 68) supergroup with approximate lattice constants a=6.42 A˚, b = 11.31 A˚, and c = 6.36 A˚ [4, 70]. These lattice constants were used asa guidance for the crystal lattice structure detailed in Figure 1.8 and in definingterraces during the experiment as shown in Chapter 3.Figure 1.5(a) shows an angled side view of the PtSn4 unit cell while Fig-ure 1.5(b) shows the incident b view of 2 unit cells along the a and c directions4Figure 1.5: (a) A slanted side profile of a PtSn4 unit cell showing bonds toeach atom’s nearest neighbors. This reveals a plane halfway down theunit cell in between two Sn layers that makes PtSn4 a good candidatefor cleaving. (b) An incident view of the surface of the PtSn4 unit cell.Figure 1.6: Renderings of PtSn4 normal to the cleaving surface. (a) Incidentview of half of the unit cell along the b direction. (b) Incident viewof the first two layers of the unit cell consisting of only Sn (top layer)and Pt (second layer). (c) First two layers of Sn and Pt showing nearestneighbor bonds.and one unit cell along the depth of b. The PtSn4 unit cell is vertically comprisedof two halves, each consisting of a Sn layer, then Pt, then another Sn. The first halfalong the b incident view is shown in Figure 1.6(a). Figure 1.6(b) and (c) showthe first Sn and Pt layer of the unit cell with (c) showing the Sn nearest neighborbonds. All Sn layers have a Shastry-Sutherland lattice (outlined in Figure 1.6(c) bysaid bonds) and the square lattice of the Pt layer is ordered such that each Pt atomis centered within every square of the Shastry-Sutherland lattice. Each Sn layer5is identical except for their translational displacement from one another, and thesame goes for the Pt layers. The Sn layers have an integer translational displace-ment of half a unit cell in either one of or both of the a and c directions, dependingon the layers being compared. The Pt layers also have a translational displacementof a half integer unit cell in either the a or c but not both. This means over a wideenough area each Sn and Pt surface on average would appear respectively identicalon a scale of several unit cells across.As previously mentioned, the c axis incident view (side view) of the unit cellcan be divided into a top and bottom half (see Figure 1.7), with both halves con-sisting of a Pt layer sandwiched between two Sn layers. This structure suggestsa cleavage plane between the two Sn layers where no Pt separates them. This isthe largest gap between any two layers in the unit cell which implies the weakestbonds and therefore the most likely cleavage plane. The halves were referred to inascending alphabetical order, while the first layer of Sn in each half was denotedSn1 and the second layer Sn2. As seen in Figure 1.7, the first layer starts at a Sn1atermination with the next layer being Pta, then Sn2a. These three consist of onehalf. The next layer down after Sn2a is Sn1b. Following that is Ptb, Sn2b, thenSn1c, Ptc and so on. Referring to Figure 1.5(a) the suggested cleavage plane can beseen between Sn2a and Sn1b where the distance between the two layers is 2.79 A˚.More detailed distances between layers are outlined in Figure 1.8. Throughout thisthesis Sn is shown as the larger, purple atom graphic and Pt by the smaller, silverone.STM is a surface sensitive technique unable to permeate deeper than a fewangstroms into the material. Even though STM cannot penetrate past a short depthit is able to scan surface areas on the order of 100 nm2. Therefore STM has theability to image a wide area on an exposed layer (also referred to as a terrace) butis limited to only collecting information constricted to the surface. For this reasonlarge overlays of just the first two layers of the unit cell were used to characterizethe crystal lattice. The broader labeling scheme illustrated in Figure 1.8 was usedto compare scans with multiple step edges and not used on singular terraces. Astep edge can be described as a sudden end of one layer within the unit cell and thebeginning of a different layer. If a scan shows two separate plateaus at differingheights, the sharp contrast between the two plateaus (or terraces) is called a step6Figure 1.7: A side profile of PtSn4 denoting the labeling mechanism usedand often referred to throughout this work. The unit cell is visuallydivided by Sn2a and Sn1b. This spacing holds promise for a dependablecleavage plane.edge. Because the two halves of the PtSn4 unit cell have the same structure, therewere only a total of three possible terraces that were expected to show differingspectroscopy and/or topography as opposed to the six layers defined in the unitcell. The three layers of interest are Sn1, Pt, and Sn2 of any singular half unit cell.1.2.1 The sample in this workThe PtSn4 sample used in this experiment was grown via a metallic self flux methodin house by the Hallas Group then placed into an ultra high vacuum (UHV) envi-ronment where it was cleaved and scanned in situ. It exhibits a residual resistanceratio (RRR) exceeding 1000 for a 0.2 mm thick sample. A material’s RRR is foundby dividing its resistivity at room temperature by its resistivity at the lowest mea-sured temperature, say RRR = ρ(300K)ρ(TLow) . This means in the absence of a magnetic7Figure 1.8: A side profile of PtSn4 with common spaces measured and listedaccording to references [3, 4, 70]. The most probable cleaving planeoccurs between Sn2a and Sn1b where no Pt layer separates them.field and at low temperatures (approximately 2 K) PtSn4 has a low resistivity. Thisvalue is comparable to what has been reported in the literature [4]. A high RRRvalue suggests a remarkably low defect density.1.3 Goal of this thesisA pattern has emerged correlating XMR and topological materials in recent history.However it is possible for a material to have excellent electron transport due toreasons that are anything but topological [71–75]. A high RRR indicates a lowresistivity at the lowest temperature. This suggests electrons are flowing freely withfew scattering events to cause a loss in momentum [38]. Therefore a high RRR isindicative of excellent electron mobility which can be caused by low defect density.XMR can signify the existence of many effects such as topological surface states,good electron-hole compensation, high mobility, and more [76]. The flat layered8Figure 1.9: The PtSn4 sample scanned on in this work before cleaving.This sample was grown by the Hallas Lab at the University of BritishColumbia. Sample grown and photo taken by PhD student SamikshyaSahu.structure of PtSn4 could possibly host a defect resistant layer which would allow fora path of least resistance leading to efficient electron transport. The sample couldbe extremely pure with very few native defects, or a topological surface state canbe dominating all of the above. PtSn4 has both XMR suggested to be due to a mixof e−h compensation and a d− p orbital mixture [56] as well as high RRR [4]. Sowhat exactly is the mechanism primarily responsible for these effects? How muchof a role does defect density play in the RRR? The goal of this work is to use STMand STS to dive into the mysteries behind the high RRR in PtSn4, determine thethree different cleaving planes, analyze common defects seen and present a solidfoundation for any future scanning probing microscopy (SPM) work on PtSn4.STM is a viable candidate for exploring these questions as it allows direct ac-cess for viewing and studying materials in real space. STM is a powerful toolto calculate defect density, deduce specific lattice sites responsible for possibledefects, locate the layers they reside on, as well as probe both occupied and unoc-cupied orbital states.1.4 Thesis overviewThis work discusses the exploration of topological semi-metal PtSn4 via STM andSTS divided into four main chapters of content. Chapter 2 explains the experimen-tal details of the equipment used and the science that makes them possible. It out-9lines the necessary components of STM, how it is possible to capture topographicimages and probe energy states as well as discusses the intertwined relationshipbetween the two. Chapter 3 discusses PtSn4 on the nano-scale. The three differentpossible cleaving surfaces are documented topographically and spectroscopically.Chapter 4 examines the material on the atomic scale, diving into each type of de-fect observed over the course of the 6-month long experimental run. Five differentshaped defects were found and imaged. Although most do not have enough data toconfirm their sources, probable causes are proposed for most. This hopefully willaid in future calculations to confirm how many defects are absorbates/adsorbatesversus impurities intrinsic to the growth of the material. Chapter 5 analyzes onespecific defect and the interesting behavior it presents and proposes a probable hy-pothesis explaining said behavior. Lastly the conclusion discusses future endeavorson the materials, and what next steps are recommended after the findings of thiswork.10Chapter 2Methods2.1 The history of the scanning tunneling microscopeIn the late 1970’s, physicists Gerd Binnig and Heinrich Rohrer decided to take thescience of quantum tunneling and apply it to a vacuum [77]. They discovered thatnot only could this technique acquire spectroscopic data, but also high resolutiontopographic images of materials. Thus, the first STM was invented and earnedthem the 1986 Nobel Prize in Physics [78, 79]. Over 40 years later, somethingthat “should not have worked in principle” now has given the scientific commu-nity boundless insight into interesting material physics; ranging from measuringshifting Landau levels, documenting quasiparticle interference, superconductinggaps, manipulating atoms on a material’s surface, scanning in extreme environ-ments such as milikelvin temperatures and magnetic fields up to 20 T, to imagingbiological molecules and enzymes [79–88].2.2 The physics behind STMThe basis of STM centers around the disparity between classical and quantum me-chanics, specifically quantum tunneling. Quantum tunneling is strictly a quantummechanical phenomenon where atomic particles can simply “appear” on the op-posite side of any type of barrier. This is much less intuitive than classical me-chanics. In classical mechanics a basketball thrown against some kind of barrier,11say a brick wall, with kinetic energy Tbasketball will bounce against the wall if thestrength of the wall, say Ubarrier is less than the incoming energy of the basketball,or Tbasketball <Ubarrier. If Tbasketball >Ubarrier, then it is expected that the basketballwill break through the barrier and to the other side, destroying it in the process.Figure 2.1: A set of cartoon images providing an analogy of classical me-chanics. (a) If the energy of the basketball is less than the energy re-quired to keep the brick wall together (ie, Tbasketball <Ubarrier, the bas-ketball will not penetrate the brick wall. (b) If Tbasketball >Ubarrier, thenthe energy will go into destroying the brick wall and the basketball willbreak through.For most of human-kind’s venture into physics this classical approach neverposed a problem. It covered gravity, invented steam engines, engineered worldwonders, and propelled technology forward until the turn of the 20th century.At this time, modern physics was making exponential progress [89–93], includ-ing Louis de Broglie advancing the notion that particles exhibit both particle andwave-like behaviors [94]. Two years later Clinton Davisson and Lester Germerperformed a version of Young’s famous double-slit experiment with an electrongun and confirmed the hypothesis of wave-particle duality [95, 96].Wave-particle duality is the term used to describe the fact that every object —big or small — has both wave-like and particle-like properties. Objects of classi-cal sizes, such as a basketball, are too massive for their wave-like properties to benoticeable. However objects at the atomic level, such as electrons and photons, ex-12hibit both particle and wave-like properties. If Young’s double-slit experiment wasrepeated with basketballs, classical physics would dictate the basketballs would hitthe backdrop exactly where the slits allowed them to go without much deviation(see Figure 2.2). Intuitively this makes sense, but what if the basketballs passedthrough the two slits and imprinted a diffraction pattern on the backdrop? Thisis completely unintuitive, however if basketballs were small enough for the lawsof quantum mechanics to dominate (as in shrunk down to the size of an atom)this is exactly what would happen. In quantum mechanics, the basketballs wouldcreate an interference pattern on the backdrop that goes beyond the trajectory theslits were assumed to allow, as fictionally shown in Figure 2.2. Thus confirming awave-like nature of quantum particles in addition to their particle-like behavior.Figure 2.2: A set of images implying that basketballs are traveling throughtwo vertical slits in a brick wall (one can imagine many basketballsbeing thrown incident onto the brick wall). (a) In this classical anal-ogy, the basketballs on the correct trajectory can be expected to travelthrough the slits and hit the backdrop in a way that mimics the shape ofthe slits as highlighted in blue. (b) If the basketballs behaved like quan-tum particles then upon traveling through two slots they would create adiffraction pattern on the backdrop, similar to how waves would. Thisresult isn’t seen of macrosized objects such as a basketball but is exactlyhow smaller objects function where quantum laws dominate over clas-sical ones.Wave-particle duality plays an important role in quantum tunneling. All par-ticles have a wave function describing their position in time and space, denotedΨ(x, t) which satisfies the Schro¨dinger equation,13i}∂Ψ(x, t)∂ t=[− }22m+U(x, t)]Ψ(x, t) (2.1)where } is Planck’s constant, m is the mass of the particle in question, and U(x, t)is the equation that resembles the barrier of potential energy of the system the par-ticle is in (it should be noted that this is the one-dimensional Shro¨dinger equation,but the equation can be described in two and three dimensions). U(x, t) could beanything from 0 (i.e. free particle), an infinite well, or a barrier with finite width,such as a brick wall. If enough of the wave function of the particle extends into andpast the barrier U(x, t) at the right time, quantum tunneling will take place. It doesnot travel through the barrier as it would in the classical basketball analogy, whichwould destroy the barrier. It simply appears on — or tunnels to — the other side.Figure 2.3: (top) Cartoon example of an electron tunneling through a bar-rier. (bottom) Analogous wave equation of the same transmission phe-nomenon. In both cases the wave equation becomes a decaying expo-nential inside the barrier and resumes to oscillatory behavior past it.142.3 The components of an STMAn STM is an experimental machine that can consist of many parts, but the spiritof the machine includes an atomically sharp metallic tip almost touching (as in afew nanometers away) a conducting sample of choice. Both of these are connectedvia some kind of circuit that a voltage bias can be applied to in order to drive thecurrent. The tip then “scans” across the surface where the amount of electrons tun-neling is recorded and mapped out onto a 2D topographic image, hence scanningtunneling microscope.The part of the STM where the tunneling takes place is in between the STM tipand the conducting sample of choice, which is referred to as the tunneling junction.Electrons jump across a UHV barrier, or Uv(x, t), and appear in the sample wherethey are energetically allowed.An STM implements quantum tunneling by integrating the tunneling junctioninto part of a circuit. It has an applied voltage referred to as Vbias and an inter-nal resistance integrated into the circuit. Uv becomes stronger the farther away thetip is to the surface of the sample. Consequently the probability of electrons tun-neling decreases, effectively increasing the resistance of the circuit. Since VBias isnot changing, the increase in resistance is compensated for by decreasing current.When Uv is too large, quantum tunneling does not take place and no current flows.When Uv is small enough, the majority of electrons can tunnel through the tunnel-ing junction, and the circuit has a low resistance and is effectively connected eventhough the tip and sample are separated by, albeit a smaller,Uv. On a homogeneoussurface the closer the tip is to the surface, the smaller Uv, the less the resistance ofthe whole circuit, and thus the stronger the current.2.3.1 Key requirementsSTMs in practicality have many requirements to perform at the level of depend-able research, such as UHV environments, low temperature tunneling junctions of-ten supplied by liquid helium, vibrational dampening equipment, and soundproofrooms to name a few. For an STM to discern atoms, there are 4 key elements thatmake scanning with atomic resolution possible.1. Applied voltage in DC circuit15Ohm’s law dictates V = IR, or the voltage equals the current of a circuitmultiplied by the resistance of the circuit. An applied voltage in a circuitdrives the flow of electrons, or in other words, creates current. The tip cannottunnel if no current is able to flow. Without an applied voltage, no electronswould travel from the sample to the tip (or vice versa) even if the tip istouching the sample (what is referred to as “crashing”). Running an STMcircuit without an applied voltage is the same as attempting to turn on aflashlight without a battery. There’s no power driving the circuit.2. Feedback loopFor a given applied voltage, the further away the tip is from a conductingsurface, the weaker the signal of tunneling electrons is. Therefore, if the tipis far, the current is small since the vacuum barrier is effectively adding re-sistance to the circuit. If the tip were to approach the material and decreasethe width of the vacuum barrier, the resistance would decrease and the cur-rent would increase as a response. This is the basic idea behind the feedbackloop STMs use to move across a surface without hitting it and “crashing.”An STM feedback loop works by attempting to keep a chosen current value,called Iset , constant while it’s scanning. When the STM tip approaches afeature on the surface that registers as closer to the tip, the current will natu-rally increase. The feedback loop tells the tip to withdraw in the zˆ directionto increase the distance, thus decreasing the current back to Iset . Figure 2.4depicts this feature.In addition to the feedback loop that fine tunes the motion in the zˆ direc-tion, STM tips have piezoelectric motors that allow for extremely fine tunedcontrol of the tip. Certain voltages applied to the piezoelectric material willexpand or contract the material depending on said voltage. Setting up athree-paired system of piezoelectric motors around the tip-holding mecha-nism shears the tip in a full three dimensional range of motion, controllingthe tilt of the tip. This shifting of angles allows the tip to tilt in certaindirections and repeatedly tilting back and forth produces the scanning mo-tion. This allows for fine tuned control on the scale of picometers with adrawback being that piezoelectric materials undergo relaxation after being16Figure 2.4: A diagram demonstrating how the tip moves across the surfaceof a material. Re f f is the internal resistance of the STM circuit andVbias is the voltage set by the user. (a) The tip is scanning on a singleterrace and the incoming current Iset = Io. (b) The tip approaches anew terrace, shortening the distance from the tip to the sample. Thisincreases the live current, where Iset < Inew as well as the previous Io.This is because znew < zo as a result of the approaching terrace. (c) Thefeedback loop intakes this new information and raises the tip in the zˆdirection, restoring the distance to zo thus setting the incoming currentback to Iset . This movement in the zˆ direction is recorded and displayedas a topographical map (diagram is not to scale).activated. This results in a drifting effect when scanning over a fixed area foran extended amount of time. Editing drift correction parameters in the STMsoftware as well as scanning over the area of interest for an extended periodof time resolves this issue.3. Atomically sharp tipAn STM is capable of recording images of material surfaces with a resolu-tion on the order of angstroms. In order to achieve such fine resolution, theflow of electrons between the sample and material needs to be as precise aspossible. This importance can be shown mathematically by approximatingtwo different STM tips as conducting solid spheres; once with radius a, theother with a much smaller radius b, charges qa and qb respectively, and sepa-rated by a distance d where d a and b. For simplicity, both these tips exist17on the same material so they have the same electric potential, V , on theirsurface.The electric field, ~E, on the surface of these spheres is given by the formula~E1 =14piεoqaa2(2.2)and~E2 =14piεoqbb2(2.3)of spheres a and b respectively. Since the potentials are equivalent,Va =14piεoqaa=Vb =14piεoqbb(2.4)which can be ratioed and simplified toqaqb=ab. (2.5)Dividing the electric fields and then plugging in the previous equations leadsto~Eb~Ea=ab(2.6)where b < a, therefore ~Eb > ~Ea. Thus, the smaller the edge of the tip, thestronger the electric field. A stronger electric field calls for a more concen-trated and precise flow of electrons between the sample and the tip, whichleads to crisper more detailed data. The smallest the tip can realistically beis one atom wide, hence why an atomically sharp tip is the best case scenariofor STM experiments. That being said, the tip can macroscopically appearblunt but still be atomically sharp as depicted in Figure 2.5. A caveat to thiscondition would be a less stable, inconsistent (less “trustworthy”) tip. A lim-itation that should be noted is if the electric field reaches a certain magnitude18it can possibly influence the physics of the material within the vicinity, aswill be further detailed in Chapter 5.Figure 2.5: (a) A picture of the tungsten (W) STM tip through a microscopetaken June 17th, 2021, just before being inserted into the STM. Thistip was used to take a majority of the data described in this work. (b)The same tip after being used by the STM for six months, taken midDecember 2021. Even though the tip in figure (b) is noticeably shorterand more blunt, it is still possible to get one atom dominating the edge ofthe tip, allowing for atomic resolution. (c) A zoomed in representationof what the atomic surface of the tips in both (a) and (b) could look likeon the surface.STM tips undergo many steps of preparation before they are ready to scan.At the end of the day, as long as the surface of the tip closest to the sample19has a singular peak of atoms and there are no other peaks nearby, this issufficient enough to acquire atomic resolution on the material in question.4. Conducting sampleIf the tip is approaching an insulating sample or region, electrons will nevertunnel across the vacuum barrier. In this scenario, the potential barrier in-cludes the vacuum as well as the insulating region. This would be equiv-alent to a barrier that is orders of magnitude thicker as opposed to the fewangstroms where tunneling is achieved. STM is a surface sensitive tech-nique, meaning only the surface needs to be conducting for a material to beSTM compatible. This is exactly the case for topological insulators, wherethe bulk is insulating.Although these are just four requirements to successfully perform SPM mea-surements on a material, a commercial STM equips many more tools to obtainusable data. Since the tip is moving a few nanometers above the surface of the ma-terial, the vibrations of smallest magnitude can affect the images. Zero vibrationalnoise and a tunneling junction temperature of 0 K is experimentally impossible soscientists use a wide variety of equipment to offset these noise sources. Some in-cluding sound proof rooms, isolator legs, air pistons holding up a floating cementblock, liquid helium cryostats, ultra high vacuum environments, and more.2.4 Topographic measurementsBefore discussing how an STM records topography, it’s important to clarify that areal STM derives all data — topographic and spectroscopic — from the current.This means the recorded tip to sample distance of a scan shows a spectroscopicinfluence. To help clarify the language when discussing “tip height,” h will denotethe height from tip to scanning area while z denotes the vertical position of the tiprelative to some topographic 0 point on the scan, often referred to as the zˆ profile.The term vertical distance refers to the height of a feature on the surface relative toanother feature’s height.In this section on STM topography, the focus is vertical tip movement whereh remains constant. In this case of h remaining constant, it is assumed there are20no spectroscopic influences and the recorded differences in the value of z reflecttrue physical vertical changes. Spectroscopic factors are addressed in further detailtowards the end of this chapter after covering spectroscopy. Observed effects ofthis in the data are discussed in Chapter 3.The STM tip scans a chosen 2 dimensional area one line at a time. As it scans,the feedback loop will cause the STM tip to increase or decrease the h value de-pending on how much current the tunneling junction is drawing. If the tip ap-proaches a larger object or step edge of a homogeneous area, the current will riseto a value above Iset and the tip will increase h as a response. These changes in hare recorded in the zˆ profile of an image and this zˆ profile can be plotted topograph-ically. The result is a topographic image where brighter areas denote features thathave a more positive zˆ profile relative to other colored areas of the image.Not all atoms rest at the same vertical level within a surface — atoms canexist in differing planes, have different sizes, and varying distances between it’sneighbors. As a result, the STM tip will sense a periodic variance in current as ittravels across an atomic lattice. The feedback loop will instruct the tip to verticallymove in a periodic fashion relating to the crystal lattice spacing in an attempt tomaintain Iset . The STM again records the zˆ profile information and portrays it ina 2D topographic map of the surface, which in this case would show some sort ofperiodicity.2.4.1 Double and multi-tipsAt the simplest level, an STM converts the reaction of the tip changing current intoa topographic map. This portrays STM work as straightforward when in practiceit can take weeks — even months — to get an STM in stable enough conditionto dependably scan. The main roadblock often being problems with the STM tip.Turns out trying to craft a singular atomically sharp tip is quite arduous. In theprevious section it was mentioned that a singular peak of an atom on the surfaceof the tip is needed to gather usable data. When an STM tip has a “double” or“multi-tip,” the data results in a doubling of features. The shape and sharpnessof the peaks on the tip strongly influences the electric field and thus the resultingimages gathered.21atip shape resultant defect scan resultant step edge scanbFigure 2.6: (a) A representation of the real surface the tip is scanning, both adefect (left) and a step edge (right). (b) A chart showing what differenttopography looks like based off of tip shape. The first row is data thatis to be expected from a singular, atomically sharp tip, where one defectand one step edge is correctly shown in the second and third columnrespectively. In rows two, three, and four, the effects of a smaller secondtip, an identical second tip, and a blunt tip are shown.22Features are duplicated when there are multiple tips because electrons will tun-nel from each tip separately. If there are two peaks of atoms on the tip’s surface,say tip A and tip B, each tip will feel it’s own rise in current when it approachesthe same feature. These two “sub-tips” are both connected to the overall feedbackloop and STM, so the STM receives information of the current jumping up in valuetwice. The tip will then be told to increase it’s h distance in the zˆ direction twice,and that topographic data is saved as two separate higher portions of the surface,when in reality only one exists.The type of features, some denoted in Figure 2.6, that are duplicated dependson the h value between each multi-tip and the scanning material. If the distancefrom sample to tip A, defined as hA, is comparable in length to the distance fromthe sample to tip B, hB (say ∆h ≡ |hA− hB| x 0 nm), then features of a similaror larger size than ∆h on the lattice will show up as double. This includes largefeatures on the scale of a few nanometers, such as step edges, as well as smallerfeatures like textured defects and mounds of dirt.If ∆h is larger than a few nanometers, then the STM will not show double ofsmaller defects and lattice structures but will show double of larger terrace steps.Depending on whether or not the step edges are ascending or descending in accor-dance to the respective approaching order of the tips, it is possible that a smallersecondary tip will not pick up on a step edge at all. If the smaller tip approachesa descending step edge before the primary tip, the h distance can be too great forthe smaller tip to tunnel. However if the smaller tip approaches an ascending edgefirst, h is shorter and tunneling will definitely be achieved resulting in a double stepedge. This can be seen in Figure 3.6 and Figure 3.9 in Chapter 3.Possible resultant scans from double tips with ∆h ≈ several angstroms and∆h≈ 0 A˚ are illustrated in Figure 2.6(b) rows two and three respectively. These arejust a few examples using a double-tip when in actuality it is possible to have threeor four (or even more!) sub-tips resulting in an utterly confusing image caused bywhat is referred to as a multi-tip.Just as often as a tip can have multiple peaks creating conflicting images, thetip can also have none, which is referred to as a blunt tip. Blunt tips have theopposite affect as a multi-tip with a large ∆h. It lacks the definitions to pick up onfiner details such as the crystal lattice or defects, but is able to pick up large step23edges. This is shown in the last row of Figure 2.6(b).Figure 2.7: Early scans of PtSn4 during tip preparation showcasing classicmulti-tip scans with (a) showing a double tip and (b) showing multiple.Having a multi-tip is not the end of the world. Many steps can be taken toremove excess tips, some more extreme than others. The most common methodis called pulsing. When pulsing the tip the Vbias jumps to a predetermined value,usually much larger in magnitude than the scanning bias, for a period of time typ-ically on the order of 10’s to 100’s of ms. This “shocks” the tip and can oftenshake off loose hanging atoms or dirt. Another tactic is scanning on a differentmaterial, usually metallic gold. Gold is a soft, well conducting metal that can bepurposefully crashed into in an attempt to reshape the tip. Gold also has simpleand well documented features. It offers a good baseline for comparison and canbe easily implemented into the STM near the material of interest for some STMs.This allows for quick turn around time from tip prep to experimental scanning. An-other method, called field emission, requires setting Vbias to large values. Having alarger voltage bias allows a current of multiple orders of magnitude higher than thestandard Iset to be used. This induces a strong electric field around the tunnelingjunction and reshapes the tip. Field emission can be performed easily at a rangeof 7 - 10 V for quick tip treatment. More stubborn tips may require a high voltagepower supply to set the voltage to around 103 V. Both of these cases of field emis-sion require the distance from the tip to the sample to be increased. The higher thevoltage, the bigger the distance required.242.5 Spectroscopic measurementsThe ability for particles to quantum tunnel provides the basis that allows STMs towork. The fact that electrons are the particles that are tunneling adds a second layerof use to the mechanism. Electrons are fermions, meaning they follow the Pauliexclusion principle, where no two electrons (with the same spin) can exist in thesame state at the same time.As a unique consequence, electrons can only tunnel into a state in the mate-rial that is available for them to exist in and unoccupied by another electron [97].The number of available states per unit of energy is a complex function that hasa sensitive dependence on material dependent properties (in particular, the crystalstructure). A shorthand for expressing this function is the density of states (DOS)which is described by the number of available states per unit of energy per volume.At temperatures approaching zero Kelvin, only the lowest states are occupied, andthe energy of the highest occupied state is referred to as the Fermi energy, or EF .STS measurements are able to probe states above EF (i.e. the unoccupied states)to display a full picture of the DOS.The DOS is a description of how many electrons occupy different orbitals atspecific energy levels within a material. Metals have a finite amount of availablestates at EF , while insulators have none. This affects the current response at thetunneling junction where higher DOS areas trigger higher current responses whilelower DOS areas trigger the opposite. The tip also has its own DOS that must beaccounted for when interpreting the measured data. Resulting data from STM ex-periments represents a combination of the physics of the material plus the physicsof the tip. Spectroscopic data is a combination of the DOS of the material as wellas the DOS from the tip. If a tip has an unknown/complicated DOS, it becomesexacting to discern features related to the sample of interest from the tip. A tip witha constant DOS is preferred when studying the DOS of unknown materials.The Vbias is used to shift the band structure of either the tip and sample relativeto each other. If EF of the tip is higher than that of the sample, electrons will tunnelfrom occupied states from the tip to unoccupied states in the sample. If there arezero DOS for a specific Vbias, or EF , then no tunneling will occur. This is outlinedin Figure 2.8 where the DOS of a metallic tip and an insulating sample are shown.25Note that the Fermi energies themselves are not changing, but the band structuresare shifting with respect to each other. Applying a large enough positive voltagebias to the sample can create a pathway for electrons from the tip to tunnel intothe valence bands of the sample (Figure 2.8(b)). Applying a negative voltage biascan shift the respective band structure enough to access the conduction band of theinsulator and electrons can tunnel from the sample to the tip (Figure 2.8(c)).Figure 2.8: A series of graphics that shows the DOS of the tip and an insula-tor for 3 different energy levels plotted vertically. (a) A representationof a tunneling junction where the voltage bias has shifted EF of the tipto match EF of the sample. All elastic scattering processes align oc-cupied/unoccupied states from the tip to occupied/unoccupied states tothe sample respectively. Therefore no tunneling will occur. (b) A repre-sentation of a tunneling junction where a positive bias is applied to thesample allowing for electrons to tunnel from tip to sample. (c) A repre-sentation of a tunneling junction where a negative bias is applied to thesample. This reverses the flow of electrons and now tunneling occursfrom sample to tip.Electrons can only tunnel into states that exist. If Vbias is dictating the sample’srespective EF at a range where the material has no DOS such as Figure 2.8(a),electrons will not tunnel. As a result, current will not flow deeming that area of thematerial insulating. If there is a high DOS at a specific energy, the probability ofelectrons tunneling into that state increases and the resulting current rises.2.5.1 STM tunneling equationThere are several resources that cover the theory behind scanning tunneling spec-troscopy [98–102]. The reader is encouraged to explore the cited sources for more26in depth derivations as a simple review will be discussed here. The relationshipbetween the tunneling current from the tip to the sample can be approximated asfollows:Its ≈−4pie}∫ eV0|M|2ρt(ε− eV )ρs(ε)dε (2.7)where |M|2 is the tunneling matrix element, ρt and ρs are the DOS of the tip andsample respectively, and the rest are constants relating to the Fermi distributionas well as accounting for electron spin. If the DOS of both tip and sample arefairly varied as a function of energy, this integral is quite complicated. But if thematerial of the tip is cleverly chosen to have a flat DOS (such as W, Pt, or PtIr),then ρt(ε − eV ) can be treated as a constant and pulled out of the integrand. Thematrix element can also be treated as a constant since it represents a vacuum andalso be pulled out of the integrand. [102] This leavesIts ≈−4pie} |M|2ρt(0)∫ eV0ρs(ε)dε (2.8)Its ∝∫ eVoρs(ε)dε. (2.9)Performing the derivative with respect to voltage, ddV , to each side yieldsdItsdV∝ ρs(eV ). (2.10)Through some clever assumptions, a relationship between Vbias, Its, and thedensity of states is found. The derivative of an I−V curve is directly proportionalto the material’s DOS.In order to take a spectroscopic measurement experimentally, the tip stops scan-ning, the feedback loop turns off, and the tip rests at a fixed h. The STM then“sweeps the bias,” which measures the current versus bias voltage (I−V curve).A functional derivative can then be taken on the I−V curve, thus providing a dataset that resembles the DOS of the material. A lock-in can also be used to recordspectra, where a small high frequency AC modulation is applied to the DC Vbiasfrom which the current is later demodulated to reveal the dIdV [102].27The vast majority of the various spectra detailed throughout this work are av-erages of multiple spectra taken around the same area. While acquiring spectra —either I−V or lock-in — it is recommended to perform multiple measurementsaround/on the same area. The user settings of the spectroscopic measurementsallow for multiple bias sweeps within one measurement. While this helps with av-eraging the spectra, it only averages spectra from a single spot on the surface. Ifperforming spectroscopic measurements on a terrace, moving the tip to differentlocations on the terrace and averaging those spectra is preferred. When attemptingto probe a specific local density of states (LDOS), performing multiple separatespectroscopy runs around (but still on) the area of interest is beneficial.2.5.2 Grid MapsA useful tool in STM experiments is the grid map. A grid map is a 3D data struc-ture that takes a spectroscopic measurement at each pixel of a designated scanningarea. This is done by selecting a square scanning area and confirming that the tipand/or sample is not susceptible to drift. Once the area is chosen, the user candefine a resolution of a grid that overlays the scanning area. For each box/pixelin this “grid,” the tip will perform a set amount of spectroscopic measurements.The result is spectra for each pixel of a chosen STM image that can be viewed asa conductance map of the surface at each discrete voltage step used in the mea-surement. The spectroscopy itself can be pulled from the data structure, or furtheranalysis can be done, such as Fast Fourier Transform (FFT) for viewing quasiparti-cle interference (QPI). Grid maps often take over 24 hours to complete and requirea trustworthy tip, therefore they are not the most common mode of spectroscopicdata collection.2.6 Spectroscopic influence on topographic imagingAs mentioned previously, the acquired data in STM experiments is a mixture oftopographic and spectroscopic information. This interwoven relationship stressesan importance of correctly defining “height” when discussing STM. Recall thatthe physical distance from tip to sample is h while the relative vertical height, orthe zˆ line profile, is denoted by z. If there was no change in vertical height on a28flat terrace but there was a different domain with different spectroscopy, h wouldchange in size and z would reflect what could look like a plateau or a canyon, asis demonstrated in Figure 2.9. Even though the physical vertical difference of thesurface of the two different domains is zero, due to the spectroscopic influence bothh and z register and record a change.Figure 2.9: A cartoon rendition of an imaginary material showing spectro-scopic influence on topographic data. (a) Arbitrary spectra of the twotypes of atoms. (b) A singular flat terrace with an imagined domainboundary of atom B inside of an atom A domain. As the tip scansacross the flat terrace atVbias =V1, the current decreases in value, bring-ing the tip closer to the surface even though the surface is flat and hasno vertical topological variations. (c) The resultant zˆ profile from thetopographic scan of (b). Even though there is no true topographic vari-ation, the influence of the DOS of the atom B domain can create a stepedge-like feature in the zˆ profile.Scanning tunneling microscopy and spectroscopy are both governed by the tun-neling strength between the tip and material. The distance between the sampleand the tip, h, is a function of current response controlled by the feedback loop.The caveat is that areas with a high LDOS also cause an increase in current. Thefeedback loop strives to keep the tunneling current constant, so larger geometric29features as well as areas with a high LDOS will cause h to increase. Thus, the re-sultant zˆ profile data has spectral information interwoven within the topographicaldata. As a consequence, some surface fluctuations may not be as pronounced asthe topographic information claims. A surface may appear closer or farther awaythan in reality if it holds lower or higher DOS. Areas that have a higher zˆ profilemay just have a higher LDOS and the opposite holds true as well. An example ofthis is shown in Chapter 3 and the phenomenon is detailed in the cartoon diagramFigure 2.10.To illustrate the complexity of this height information, a fictional material withtwo different terraces, both with unique spectra, is presented in Figure 2.9 and Fig-ure 2.10. Two voltage biases are denoted, V1 in orange on the left, and V2 in blueon the right. The exposed surface B shows a terrace relaxation which can happenupon certain cleavage planes. Different from the piezoelectric motor relaxations, arelaxation in this context is when the distance between the terminated terrace andthe terrace underneath it shrinks because the bonds supporting the top terminationno longer exist. As a result, the top terrace falls (or “relaxes”) into the secondterrace. This is depicted in Figure 2.10(a), experimentally observed in PtSn4, andwill be discussed in Chapter 3. Terrace relaxations tend to be small (around a fewtenths of an angstrom) compared to the size of a single step edge. This informa-tion can easily become overshadowed on the recorded zˆ profile by DOS effects,complicating analysis.At theV1 voltage bias, surface A has a higher dI/dV value, DOS, and integratedDOS than surface B. Therefore, when the tip travels from scanning surface A tosurface B at Vbias =V1, there are less states for the electrons to tunnel into and thetip has to reduce its distance to the sample in order to maintain Iset . This decreasesthe h value on surface B compared to its h value on surface A. When the zˆ profileshows a step edge, this decrease in h is hidden in the zˆ profile information, creatinga false appearance of a bigger edge. Compared with V2, where the integrated DOSof the two fabricated surfaces are equal, the current will also be equal, and thus hwill be equal.In reality, the h value for two dissimilar surfaces will never be exactly the sameunless with a cleverly chosen Vbias. The h values and the recorded z values areboth a function of current from the feedback loop. The current between the tip and30Figure 2.10: A cartoon rendition of an imaginary material showing spectro-scopic influence on topographic data. (a) Arbitrary spectra of the twoterraces discussed. α(ε) represents the gray dI/dV curve of surface Awhile β (ε) the dark purple dI/dV curve of surface B. On the right, aterrace relaxation of δ A˚ is depicted. ValuesV1 andV2 are chosen where∫ V10 α(ε)dε >∫ V10 β (ε)dε and∫ V20 α(ε)dε =∫ V20 β (ε)dε . (b) Two dia-grams showing visual representations of the tip-to-sample distance h,scanning each terrace at V1 and V2 respectively. Surface B has a lowerintegrated density of states atV1 and therefore h is smaller compared toSurface A. At V2, the integrated DOS are equal. As a result, h remainsthe same and there is no change in h between surfaces. (c) Resultant zˆline profiles of diagrams in (b). The zˆ profile data withVbias =V1 showan inflated value for the step edge vertical distance due to the DOS in-fluence.sample is directly related to the integration of the DOS with respect to energy ( dIdV =ρs(eV )) as derived earlier in this chapter. The values h and z are a direct functionof current response, and the current is derived from the integrated DOS. Therefore,31the h values of different spectroscopic terraces will not be equal unless the twosurfaces have an equal integration of the DOS. In other words, the integrated DOSfrom 0 to the chosen Vbias for each surface must match for a specific scanning biasin order for the resultant h values to be comparable. In Figure 2.10, V2 does notproduce more comparable h values between surface A and B because the values onthe dIdV are closer together than they are inV1. Rather,V2 produces more comparableh values between the two surfaces because the areas underneath each respectivecurve from 0 to V2 are closer in value than that from 0 to V1. Scanning at a cleverlychosen voltage bias where the integrated DOS between the two terraces in questionare equal is the best way to minimize this effect.2.7 The STM in this workThe STM used in this work is a commercial, low temperature, ultra-high vacuumCreaTec Fisher & Co. GmbH STM. It consists of a load lock, preparation chamber,argon sputtering and electron beaming station, liquid helium cryostat and the STMscanning chamber itself, some of which are labeled in Figure 2.11 below. In thisSTM, the voltage bias is applied to the sample, meaning that a positive voltagecauses electrons to flow from tip to sample.The tip used in this work originates from a tungsten (W) wire. It was elec-trochemically etched using a potassium hydroxide solution. Figure 2.5(a) showswhat a W tip looks like after this process and before being inserted into the UHVenvironment for use. Once in the UHV environment, the tip is sputtered and an-nealed using Ar+ sputtering and electron beaming to clean and prepare the tip forscanning in a UHV environment. Once the prepped tip is inserted into the STMhead, the tip is controlled by piezo motors allowing it to finely scan and move inthree dimensions. The larger mechanism holding the tip can also move in all 3dimensions with a much greater range of motion. PtSn4 shared a sample stage withgold coin that was used for moderate tip prepping and adjustments.32Figure 2.11: A picture of the STM used in this thesis. (top) A picture ofthe front of the STM. Pointed with arrows from left to right are themanipulator arm, the prep chamber, the STM chamber, and then abovethat is the cryostat. (bottom) A picture of the back of the STM. Theload lock, its transfer arm, and the helium recovery line are labeledwith arrows.33Chapter 3Topography and spectra ofpristine surfacesOver 6000 topographic scans, 756 sets of spectroscopy (which had a any range of3 to 150 bias sweeps per file), and 10 separate grid maps were acquired on Ptsn4in the six month long experimental run. Scanning on PtSn4 consistently revealedvery large terraces with step edges being uncommon. Initially the defect densitywas quite low but increased over time. This could be a possible result of absorbatesin the STM chamber finding ways to the sample over the course of 6 months,or merely coincidental by the nature of scanning different areas of the material.The word pristine is used throughout this work to describe data that is taken onareas either absent of defects or over a wide enough range so that on average theordered crystal lattice dominates. This chapter will focus on the pristine lattice andspectra seen, while specific defects discovered will be discussed in depth in thenext chapter. All scans and spectra were taken at 4.2 K and all Iset values of STMscans were set to 600 pA throughout this work unless stated otherwise.3.1 Pristine topographyThe lattice on the most common terrace was a square waffle pattern (portrayed inFigure 3.1 and Figure 3.2) using a Vbias ranging in between -1 V and -320 mV butmost commonly scanned at -400 mV. The pattern could also be seen at positive34biases but was never easily noticeable until Vbias > +600 mV. Scanning with apositive Vbias did not show the atomic lattice with the same ease as negative-biasscanning did. Hence a majority of the topographic data was taken at -400 mV. Thesecond most frequently used Vbias was +400 mV as this voltage bias provided tipstability, and would sometimes reveal atomic structure under the circumstance thatthe tip was ultra sharp, or had some particular termination, as this happened only asmall handful of times over the course of 6 months.Figure 3.1: (a) An STM scan of a pristine surface of PtSn4 with no defects,taken at -350 mV and 600 pA. (b) Dotted lines overlayed on top of thefirst Sn and Pt layer of the unit cell. The dotted diagonal orange andstraight blue lines correspond to the solid diagonal orange and straightblue lines in part (a) respectively. (c) and (d) Height profiles of thetopography along the blue and orange lines in figure (a) and (b).According to crystallographic information [4, 70] the distance between the firstlayer of Pt atoms in the a and (−a,0,c) direction is 6.42 A˚ and 4.53 A˚ respectively.35From graphs (c) and (d) in Figure 3.1 topographic line cuts across the atomically-resolved surface are shown. The distance between neighboring troughs of theseline cuts averages out to be approximately 6.29±0.03 A˚ and 4.39±0.07 A˚ respec-tively. This is slightly smaller than the reported distances in the literature whichis a reasonable expectation due to the thermal contraction of measuring the latticepatterns at liquid helium (He) temperatures and DOS influences.An atomic overlay on a 2D Fast Fourier Transform (2D FFT) filtered image ofa pristine PtSn4 surface can be seen in Figure 3.2. 2D FFT filtering is an imageprocessing technique that performs a Fourier transform on a 2D matrix and repro-duces an image that highlights the frequencies found and reconstructs them. Thisallows for the spatial frequencies observed in the crystal lattice to be easily studied.Large tip movements can cause an excess amount of piezo relaxation that can skewthe appearance of the crystal lattice. The average distance between troughs on lineprofiles taken on the 2D FFT image show the distance between Pt atoms along thea and (−a,0,c) axes to be 6.22±0.05 A˚ and 4.43±0.03 A˚ respectively. Althoughthese values fall slightly out of range with the reported literature, it is important toremember that STM records current response (which means DOS influence) on thesurface of a material and not the physical distances of the bulk.If time does not permit for the tip to settle, filtering methods such as the 2DFFT in Figure 3.2 can be used to recover the periodicity of the crystal lattice. Drifteffects can make it difficult to align lattice sites to certain features as discussed inChapter 4.The structure of the PtSn4 crystal lattice suggests that the favored cleavageplane is in between the Sn2a and Sn1b layers. This is supported by the fact that themost common zˆ value for step edges recorded was half a unit cell. Therefore thespectrum shown in Figure 3.4 and Figure 3.5, which was also the most common,was assigned to the Sn1 termination. However, the Sn layers do not have 4-foldsymmetry while the Pt layer does. It is believed that the Sn electronic structure is“smeared” out on the surface and the black dots/holes are the spaces where Pt sitsunderneath in the second layer from the surface (i.e. dips in the Sn electron sea).This is further supported by spectroscopic evidence discussed in the next section.As seen in Figure 3.3, the chosenVbias has a large effect on not only how visiblethe atomic lattice is but how surrounding features and defects present themselves.36Figure 3.2: An overlay of the first two layers of the PtSn4 unit cell (Sn1a andPta) according to the lattice constants from [4, 70]. The STM imagewas scanned at -400 mV and 600 pA and then underwent a 2D FFTfilter. The Pt atoms align along the darker ordered spots of the image,suggesting the darker spots of the waffle pattern seen are the holes inthe Sn surface where the Pt atoms rest underneath. The blue and orangelines represent the line profiles taken on the 2D FFT image giving thePt distances to be 6.22±0.05 A˚ and 4.43±0.03 A˚ respectively.Figure 3.3: A set of STM images of the same general area taken at variousVbias and all at Iset = 600 pA. From left to right, Vbias = -800 mV, -400mV, +370 mV, +600 mV, and +800 mV. One to two defects are apparenton top of the surface.The reader is encouraged to focus on the differences in background lattice in Fig-ure 3.3, as specific defects will be discussed at length in Chapter 4. The underlyingcrystal lattice disappeared when scanning with a Vbias = -200 mV to Vbias = +500mV, and reappeared beyond that, tip shape depending.373.2 Pristine spectroscopyA tip that takes great spectroscopic data may not be successful at taking topo-graphic data, and vice versa. STM data is heavily influenced by the physics of thetip. When taking topographic data the tip can take on many different shapes andstill produce a decent image. Thus it is expected that not all spectra looks iden-tical at all times if the tip has gone under any dramatic events. The features thatstay constant in spectroscopy data are peaks, plateaus, and rises/falls that tend toremain fixed around specific voltages. Figure 3.4, for example, has two differentmeasurements of spectra taken on two separate dates, two separate areas, two sepa-rate ranges, and both on the pristine surface (although some defects reside nearby).For both spectra, there is a peak in the LDOS at 315 mV with the sharp slopeupwards at 225 mV. Note that the spectrum from image (a) in Figure 3.4 rangesfrom ± 400 mV while the spectrum from image (b) ranges from ± 800 mV. Thestarting voltage of the sweep also affects the overall magnitude of the current re-sponse, since it dictates the height (h) that the tip is fixed at for the rest of thespectroscopy measurement (refer back to Figure 2.10 for the relationship betweenDOS and tip height). If the integrated DOS at the starting Vbias is relatively high,the tip will perform the bias sweep farther away from the surface than if the DOSwas lower. This effect can be seen in Figure 3.4. The maxima of the plotted yaxes differ by a large enough amount that if they were plotted on the same axes,the spectra from image (b) would dominate the spectra from image (a), and thetwo would be visually incomparable. Both spectra dictated the tip height for themeasurement at the maximum positive biases. The DOS at +800 mV is higher thanthe DOS at +400 mV and therefore spectra taken in a range similar to image (b)will have results of higher intensity. Even though some details of the curves differfrom each other, the features agree in placement.Figure 3.5 has a spectroscopy measurement ranging from -1 V to +1 V takenon the pristine surface away from other defects. Figure 3.5 demonstrates the mostcommon spectroscopy seen during the course of the experiment, which noted alow LDOS until about +175 mV, with a sharp rise into a few separate peaks around+315 mV, +684 mV, and +945 mV respectively. On this pristine surface and withinthis voltage range, three peaks in the spectroscopy were always seen. Even though38Figure 3.4: (a) An STM scan of PtSn4 of a pristine surface with two minordefects taken at -400 mV and 600 pA. (b) An STM scan of PtSn4 ofa pristine surface with five minor defects taken at +300 mV and 600pA. (bottom) The corresponding spectroscopy measurements taken onthe blue and orange dot respectively. The transparent vertical blue linesdenote core spectroscopic features that vary minimally — if at all —due to tip shape.their heights and shapes varied greatly depending on tip events, the voltages thepeaks formed around stayed close in range.The spectra shown in Figure 3.4 and Figure 3.5 portray the LDOS most com-monly seen on this material. On very infrequent occasions however, different spec-tra (shown in Figure 3.6 and Figure 3.7) were seen. In the STM scan in Figure 3.6,terraces A, B, and D all had spectra resembling the most common spectrum shownin orange, while terraces C and E had spectra that matched the newer features ofthe secondary blue curve. In this figure and throughout this thesis the spectroscopicdata shown are color coded within each figure. Figure 3.6(a) terraces A, B and D39Figure 3.5: (left) An STM scan of PtSn4 of a pristine surface with two minordefects taken at +400 mV and 600 pA. (right) The corresponding spec-troscopic measurement taken on the orange dot. The transparent bluelines denote the voltage placement of features consistently seen in thepristine base spectrum on this surface.Figure 3.6: (a) An STM scan of PtSn4 of multiple terrace steps taken at +400mV and 600 pA. (b) The corresponding spectroscopic measurements.The orange dot denotes the spectra taken on terrace A, the blue doton terrace C. Note the vast differences in shape, implying these twosurfaces are not of the same termination type.are shown in orange while terraces C and E are shown in blue. In Figure 3.6(b) twodifferent specturm are shown — one in orange and one in blue. This is to show thatall the terraces of the same color show the same type of spectrum, indicating theyare of the same layer in the unit cell. The guidance of terrace to spectra are color40Figure 3.7: (a) An STM scan of PtSn4 of multiple terrace steps taken at +1.00V and 600 pA. (b) The corresponding spectroscopy measurements. Onetaken on terrace G, H, and J. The H terrace has two spectroscopy mea-surements, one on top of the white dots (the left most purple dot) andone not (the right most blue dot). (c) An STM scan of different terracestaken at a later date taken at -400 mV and 600 pA. (d) The spectroscopydata correlating to the dots on the respective terraces in part (c).coded within each figure and not for all figures. For instance, in Figure 3.7 the bluenoted terrace correlates to a spectrum pattern that does not match the blue spectrumshown in Figure 3.6. When terraces with differing spectra are discussed they arecoded within the respective figure by color to indicate which terraces have match-ing spectra. White and black indicators on terraces means viable spectroscopicdata was not obtained.Similarly in Figure 3.7 the blue and purple spectra taken on the H and P terracesrevealed a third, different type of spectrum. PtSn4 has three distinct terminations41where the electronic structures vastly differ from each other, and therefore wouldbe expected to show three distinct spectra, one for each possible termination: Sn1,Pt, and Sn2 (as shown in Figure 3.14). This piece of information became pivotal insolving the puzzle of mapping out the terrace correlations, and will be discussed indepth in the next section.3.3 Terrace characterizationWhen a material is cleaved, it often does not cleave along the same plane across thewhole span of the surface. Rather, different terraces are exposed, corresponding todifferent layers of atoms. The unit cell of PtSn4 hinted at an accessible cleavageplane between the two Sn2a and Sn1b layers, with the possibility of other termina-tions being exposed during the cleave. Scanning showed that the terraces of PtSn4were quite extensive and step edges seldom. Quality step edges were still found,such as that in Figure 3.8. Measuring the difference in z values from one terrace toanother and comparing that to the published distances between layers of atoms isone way to determine which surface is being scanned. Paired with the knowledgethat different surfaces have different spectra, a full picture of PtSn4 terminationscan be drawn.At first the terrace heights measured did not directly match the known inter-layer spacing of PtSn4 [4, 70] as seen in Figure 3.9, as well as the later mentionedhistogram figures (Figure 3.10, Figure 3.12, and Figure 3.13). By multiplyingthe heights measured by a factor of approximately 0.85 the correct heights can befound. A factor of 0.85 was chosen due to the fact that the most common stepheight seen was 6.64 A˚. It was inferred, due to the nature of the material, that acommon cleaving terrace would be half a unit cell, which is 5.64A˚, the ratio be-tween these two values being 0.85. STM piezos require calibration, and this ismost likely the correct calibration ratio. It will need to be confirmed by scanningon a well documented material, such as Au(111).In addition to the calibration correction, terminations of less than half integersteps of the unit cell lose the structural support that nearest neighbors were pro-viding. This causes entire terraces to “relax” into the surface (review Figure 2.10in Chapter 2). These relaxations cause step edges to appear larger in height than42Figure 3.8: A composite image of two separate scans showing a cascade ofeight different terraces in PtSn4. Both of these scans were taken with aVbias =−400mV and Iset = 600pA.studying the bulk unit cell structure would imply. Relaxations tend to cause smallchanges in z values on the order of fractions of an angstrom. Information stemmingfrom relaxed terraces and DOS influences both affect the z data and can be difficultto discern from one another.To work around this confusion histograms were taken from topographic scans43Figure 3.9: (a) An STM image of multiple step edges of PtSn4 with two linescut perpendicularly across said step edges to denote where line profiledata was sampled. The longer line cut is blue and corresponds to (b)while the shorter one is orange and corresponds to (c). (b) and (c) havetwo step edge sizes listed at each associated step. The first size is theraw data, and the second is the data after the 0.85 calibration factor wasapplied.and paired with spectroscopic information to characterize the terraces observed.Figure 3.10, Figure 3.12, and Figure 3.13 pair half integer values of the unit cellto a histogram of a scan with multiple step edges. The STM images were leveledand histograms were taken using SPM analyzing software Gwyiddion and WSxM[1, 2]. The z profiles from each pixel within a scan were taken and plotted on ahistogram of z value frequency versus the z values themselves. This provided avisual representation of the z values of each terrace with respect to one another.Each peak in the histogram represents the area of a terrace in the scan, shownin descending order. Comparing the z distances of the histogram in parallel withthe crystal lattice structure aligns certain layers within the unit cell to peaks in thehistogram. Using Figure 3.10 as an example, layers A, B, D, and F all align with theSn1 layer. With this alignment, the Sn2 layers (labeled C and E in the topographicscan) are slightly misaligned. This is expected due to the lack of bonds supportingthe Sn2 layer if its the surface termination as well as the DOS influence betweenthe two different spectra as discussed in Figure 2.10 in Chapter 2.In the histogram of Figure 3.10 terraces labeled A, B, D and F are all color44Figure 3.10: A histogram of the z profile of the corresponding STM imagematched with the vertical crystal lattice structure of PtSn4. On theright, the raw height profiles are shown as well as the corrected heightprofiles due to the assumed 0.85 calibration. This figure shows thatwhile the Sn1 is the more common termination plane, a Sn2 termina-tion is possible and also undergoes a relaxation.45coded orange while terraces C and E are color coded blue. The color codes areto indicate terraces that have matching spectra. Terraces that are color coded withwhite or black letters have no spectroscopic data to report. Terraces with the samespectrum should align with the same type of layer of the unit cell. In this histogramfigure terraces A, B, D and F all have the same type of spectrum, and all align withthe Sn1 layer. Terraces C and E have matching spectra to each other which does notmatch the spectrum of A, B, D and F. The histogram aligns both C and E terraces toa relaxed Sn2 layer. The spectrum matching was used as a guide in the histogramalignment to confirm terrace characterization. Assigning the Pt layers or the Sn2layers to the orange spectrum terraces causes misalignment for other terraces andspectra. The Sn1 alignment with the orange spectrum is the only organization thatsatisfies terrace heights and spectrum pairing. Using this knowledge paired withthe differing spectra as well as the influence the DOS can have on the recorded zprofiles, the findings of the three different types of terraces were confirmed.At first this poses a problem. According to the histogram in Figure 3.10 (andafter the 0.85 calibration), the z value in between the first Sn1 to Sn2 step edge is3.54 A˚ while the z value for the next Sn1 to Sn2 step edge is 3.46A˚. The publisheddistance between these two layers, however, is 2.86 A˚ as discussed in Chapter 1.This would mean the relaxation of the Sn2 terraces are more than half an angstrom,which is an unrealistic relaxation. However, at the end of Chapter 2 it was discussedthat STM data is influenced by the sum of topographic height and the integratedDOS at a particular Vbias. The STM topographic photo in Figure 3.10 was takenat Vbias = +400 mV. At this voltage, the difference in the integrated DOS betweenthe two different terraces is significant as depicted in Figure 3.11. Because terracesC and E have a lower integrated LDOS at the scanned voltage, h will decreasein value/the tip will move closer to the surface to meet Iset . This will register as alarger difference in height than exists in reality. The first step edge between the Sn1and Sn2 layer reports a z value of 3.54 A˚ while the known distance between the twolayers within the crystal lattice is 2.86 A˚. That leaves a difference of 0.68 A˚ that is acombination of the Sn2 lattice relaxing as well as the difference in integrated DOSbetween the two terraces, which results in a change of the distance from sample totip, h. This is a real life example of the effects explained at the end of Chapter 2 inFigure 2.10.46Figure 3.11: A segment of the spectra taken on the surface shown in Fig-ure 3.6 from +100 mV to +500 mV. The STM image was scanned withaVbias = +400 mV as denoted with a vertical double arrow. The LDOSat this particular bias varies quite a bit for the two terraces, with terraceC having the lower LDOS of the two.In Figure 3.12 the H terrace raises some questions. From looking at the imageit can be reasoned that the terrace is the Sn2 layer with Pt atoms left behind on top.DOS influence can skew this view and Pt atoms wouldn’t be expected to remain intheir fixed positions if the surrounding bonds disappeared during cleaving, a similareffect as seen in the relaxation of the Sn2 terrace. Given that both these images arescanned at different biases, discerning the cause of the dots as well as where theH terraces lies on the histograms becomes complicated. The differences in imagesize and voltage bias affects the resolution of the dots on the H terrace. This canpossibly lead to different peak placements between the histograms, confirming nosolid alignment within the unit cell. Sadly, understanding the H terrace remainsinconclusive.In Figure 3.12 terrace G was used as the baseline for flattening the image. Asseen in the histogram, the peaks become progressively less sharp as the terraces getfurther away from the top leveled terrace. This is another affect of relaxing piezomotors that control the tip. This scan is 150 nm2 and at some points scanned over47Figure 3.12: Two histograms of STM scans with step edges. The distancesbetween histogram peaks have been multiplied by 0.85 for the propercalibration. Scan (b) is a zoomed in scan of the dotted terrace in scan(a). The Sn2 terrace has an upwards directional shift in (b) due to theDOS influence effect. The H terrace remains inconclusive as denotedby the two dashed lines in the histogram in part (a).eight steps in one line. In order to scan this safely without damaging the tip, a slowscanning speed is used. This protects the tip, but allows more time for the effectsof drifting and relaxing piezo motors to arise in the data. This shows up in thedata as different terraces on vertically opposite sides of the image having differentperceived slopes to the surfaces. Therefore, the mechanism that levels one terrace48Figure 3.13: A histogram of the z profile of the corresponding STM imagematched with the vertical crystal lattice structure of PtSn4. The z pro-files in the histogram have been multiplied by 0.85 to adjust for thecalibration. The Pt lattice is seen relaxing downwards.does not level others. This is seen as the broadening of peaks the further awaya terrace exists from the one used for leveling. When the scan in part (a) fromFigure 3.12 was leveled using terrace N, peak G on the histogram was broadened.Figure 3.13 used terrace O for the baseline flattening of the zˆ values. The Pterrace was slim but showed a different type of spectrum when compared to that ofterrace O and Q. Referring back to Figure 3.7, the O and Q terraces have spectra49corresponding to the Sn1 termination. Aligning with the crystal lattice structureshows that the Pt terrace undergoes a relaxation as the DOS influence would requireh to increase in value as the tip scans from Terrace O to terrace P.3.4 Final terrace determinationsConsidering the histograms alongside the spectroscopic terrace information, it canbe concluded that the three separate terraces (Sn1, Pt, and Sn2) have been identi-fied. Sn1 is by far the most likely exposed terrace after cleaving, with its spectro-scopic features existing above +175 mV. The Pt terrace spectroscopy has a broad,shallow minimum centered roughly at zero bias. The Sn2 lattice has a broad peakcentering around -530 mV and ranging from -820 mV to -250 mV and a steepincrease into the positive range starting around +400 mV. These three spectra arecompared in Figure 3.14. There is no singular voltage bias where all three spectrahave the same integrated DOS therefore any data on step edges will have a DOSinfluence. The best values to minimize this would be around +540 mV or (an evenbetter choice) anywhere between -250 mV and +200 mV. A log plot of this rangeof the three spectra is shown in Figure 3.15 for the reader to refer to themselveswhile Table 3.1 lists suggested scanning biases depending on specific terminationsteps.Table 3.1: A table showing approximate suggestions of Vbias depending onwhat surfaces are being scanned. These biases should minimize the DOSinfluence between the corresponding terraces.Terraces in Scan Proposed VbiasSn1 and Pt ≈ -200 mV – +100 mVPt and Sn2 ≈ +650 mVSn1 and Sn2 ≈ -270 mVSn1, Pt, and Sn2 ≈ -300 mV or ≈ +600 mV50Figure 3.14: The three different types of spectra found on the three separateterraces plotted against each other. The orange medium size curve isfrom the Sn1 surface, the small blue curve denotes Pt, and the largerdark purple curve is Sn2.Figure 3.15: The three different types of spectra found on the three separateterraces plotted on a log scale from a voltage range from -400 mVto +850 mV. No voltage value permits all terraces to have the sameintegrated DOS which would negate the DOS influence.51Chapter 4Topography and Spectra ofDefectsIn Chapter 3, different terminations were discussed as a whole and compared witheach other, with scans often ranging around areas 100 nm2 or higher. On the otherhand, defects in a material occur on the scale of a few angstroms. Some defectsare a result of an atom substitution in the crystal lattice, thus distorting neighbor-ing bonds. Or in some cases it is caused by an atom missing completely, what iscalled a vacancy. Multiple types of defects on the Sn1 surface were discoveredover the months of scanning, all appearing with varying frequency and showcasinga variety of spectroscopic behaviors. Listed in increasing frequency of occurrence,and in reference to their apparent shape, they are referred to as the 4-fold defect,spearhead, crescent, butterfly, and croissant. Symmetries of defects compared withthe crystal lattice can help confirm defect sites [83]. Defects in a material canhave many causes and effects on the topography and spectroscopy. This chapterdiscusses the spectroscopic and topographic variations that the aforementioned de-fects impose on the material’s surface and discusses possible causes and potentiallattice site locations for such effects. Defects are discussed in order of rarest to mostcommon in occurrence, and were all observed on a Sn1 termination. The spectro-scopic data in this chapter originates from a combination of point spectroscopymeasurements and grid maps.524.1 4-fold symmetry defectThe rarest defect seen in the 6 months of scanning was this 4-fold symmetric defect.A 5 nm2 scan will show on average about 530 Pt sites, while areas ranging from 3nm2 to 150 nm2 were used in recording the 6000 scans obtained. Not all of thesescans were viable, nor were they scanned at a resolution to discern defects (suchas the terrace scans in Chapter 3). Even so, this still leaves a couple thousandscans where viewing this defect was plausible, yet it was only seen on two separateoccasions over the total run time of this experiment. The Sn terraces of the materialdo not have any sites with 4-fold symmetry, while the Pt terrace has purely 4-foldsymmetry. Therefore, the 4-fold symmetry of this defect confines it to the Pt layer.In Chapter 1, the high RRR of the material was noted as a strong indication that thematerial had very few intrinsic defects, or that another effect was responsible forthe high mobility. The rarity of this defect aligns with the notion that a low defectdensity is partly responsible for the high RRR.4.1.1 4-fold topography and spectroscopyA grid map was performed on the second appearance of this defect, and spectraderived from this map are shown in Figure 4.1 and Figure 4.2. Each spectrumshown is an average of 5 spectra pulled from the same area. The spectra on topof the defect as well as on its left, right, and bottom lobes show a flattening of theinitial trough at around +500 mV. The lobe directly above is a slightly dampenedversion of the pristine spectrum, both of which have the valley at +500 mV restored.On all areas on top of and around the defect, the spectra aligned with the Sn1layer and no shifts were noted. The defect also did not have any major appearancechanges for a wide range of Vbias. Whether scanned at +600 mV or -600 mV, thereremained a dark hole in the center.The 4-fold defect does not vary in appearance throughout a wide range of volt-age biases. This means that the change in h as the tip travels across the defectremains about the same no matter the voltage bias. This indicates that the changesin h could be an effect from a physical lattice distortion, or the magnitude of DOSinfluence spans equally across the range of voltage biases used. Given the strongsimilarities between the defect center, defect lobes, and pristine spectra as well53Figure 4.1: (a) The first recorded instance of the 4-fold defect. (b, d-f) Thesecond recorded instance of the 4-fold defect shown at multiple voltagebiases. There was a month and a half of time in between these two oc-currences, and tip shapes were drastically different at the two times. (c)Spectra taken on the center of the 4-fold defect plotted against the pris-tine background, with the difference between the two curves in black.as their similar magnitudes, any DOS influence on the topographic image will besmall (spectra pulled from grid maps were all taken under the same conditionstherefore their magnitudes are comparable).In regards to a physical distortion, the width of the entire defect spans about2.5 nm. This is considered a very large area for a vacancy. A defect on a Pt latticesite could be inducing strain on the lattice around it. This is consistent with thedifficulty the Hallas Group has experienced in doping Pt lattice sites of PtSn4, butfurther exploration is needed to support this hypothesis. Figure 4.4 shows a lineprofile of the recorded z data across the defect. The lobes have a peak 6 pm abovethe relative surface and the center has a z value of about 12 pm below relative tothe surface. 6 pm could very well be due to a DOS influence that is too subtle inthe spectra to see. Given the similarities in all the spectra on top of and around thedefect, DOS effects may not be the primary cause for the appearance of this defect,54Figure 4.2: Spectra on the four bright lobes of this defect plotted against thedefect center and pristine spectrum. The first valley of the center andbottom lobe (around +500 mV) appears flattened compared to the otherlobes as well as the pristine. No notable shifts are detectable, and thespectra closely resembles the Sn1 terrace spectrum.Figure 4.3: Spectra ranged from -1.0 V to 0 V pulled from the grid map ofthe 4-fold defect plotted on a log plot. The log plot reveals no obviousfeatures in the negative energy region. The dI/dV curve from the centerof the defect crosses over the pristine spectrum at approximately -550mV.but can still play an important role. It is possible some sort of hole exists on thissite, but further analysis is needed before any statements can be made on the causesof any physical features this defect may have.55Figure 4.4: A line profile of the recorded z height taken vertically across the4-fold defect. The depth of the center of the defect relative to the surfaceis approximately 12 pm. The recorded z profile of the peaks above andbelow the defect is about 6 pm.4.1.2 4-fold lattice overlayFigure 4.5: An image of the 4-fold defect with an overlay of the first two lay-ers of this scan’s termination. Using what is known from the croissantdefect detailed later in this chapter as well as the guide of the darkerspots of the image, the overlay suggests a Pt atom is expected to rest inthe center of the 4-fold defect.56Figure 4.5 shows a lattice overlay on top of the 4-fold defect. Tip condition andpiezomotor related drift made aligning the crystal lattice to the scan difficult. Byusing the lower left defect (the croissant defect) as a guide for alignment (discussedin detail later in this chapter) as well as attempting to line up the white Pt atomson top of the darker spots in the STM scan, we can conclude a Pt atom sits in themiddle of the 4-fold defect. Furthermore, the lobes of the defect align with thetracks of Pt atom rows that span from the proposed missing defect at 90o integerrotations from each other lobe. The second nearest Pt atoms are centered in thelobes of the defect suggesting a charge transfer to neighboring Pt atoms.4.2 Spearhead defectThe second rarest defect found was the spearhead defect. At first glance it hassimilarities to the later discussed butterfly defect, but upon closer observation thespearheads have a completely different spectroscopy. In Figure 4.6(a) and (b) thespearhead and butterfly defects can both be seen in the same scan and showcasedifferent features as the same Vbias. The spearhead defects are the top three defectsin the upper right corner of the scans in the aforementioned figure. The spear-head defects have a pointier shape with darker edges coming together to a pointunderneath their center, hence the name spearhead. These defects did not appearsignificantly more frequently than the 4-fold defects and are also considered rare.4.2.1 Spearhead topography and spectroscopyThe set of spectra exhibited in Figure 4.7 were pulled from a grid map rangingfrom -400 mV to +400 mV. The three spearhead defects were only seen within onemap and were not observed again, so there was no other opportunity to acquire alarger range of data with a more stable tip. Since all the spectroscopic informationpresented here was taken within one grid map, differences in dI/dV magnitude forthis data set are worth paying attention too. When compared to the backgroundspectrum (Sn1 surface), the initial +315 mV peak of the spectrum taken from thecenter of each defect is diminished, but still notes a rise at the same voltage valueas the pristine surface does (+315 mV). Because all spectra was acquired by thesame tip in the same conditions at the same time, this suppression of the peak is57Figure 4.6: Various topographic STM scans of the spearhead defect at differ-ent Vbias. (a), (b) Scans with Vbias = +1.0 V and +400 mV respectivelyshowing the three spearhead defects in the top right corner with two but-terfly defects in the bottom half of the photo. (c), (d) Cropped imagesof (a) and (b). (e) Scan of defects atVbias = -400 mV. At negative biases,the spearhead defects appear as bright circles indicating a higher LDOSat this negative range. At +400 mV the defects resemble spearheadspointing downwards, and at +1.0 V appear darker and more symmetri-cal.valuable information. The rest of the spectra (mostly in the negative bias range)taken from the center of the defects matches the background spectrum.Figure 4.8 shows the spectra taken from the center of a spearhead defect aswell as two darker lobes that appeared topographically on a slight angle, as seenin Figure 4.6. The spectra for these lobes aligns with the pristine spectra in thepositive range, and the peak at around +250 mV is only slightly suppressed unlikethe center of the defect. The negative bias range on the other hand tells a different58Figure 4.7: Various spectroscopic measurements of the three spearhead de-fects. (top left) STM scan of the surface the spectra was taken on. (topright) the LDOS of the center of each defect. (bottom) The spectra ofeach center defect plotted with the pristine background.story. While the center of the spearhead defect and the pristine spectra match fornegative biases, for voltage values less than -100 mV the lobes of the defect havea noticeably larger dI/dV response. This is contrary to the spectra of the butterflydefect as shown in Figure 4.20.At first glance the negative bias peak of the lobes of this defect are reminiscentof the Pt terraces discussed in Chapter 3. Figure 4.9 plots the Pt spectra from theprevious chapter against the spectra of the defect on both a linear and log scale.The log scale reveals differing features between the spearhead center and the lobe.In contrast to the spectrum on the spearhead defect, the Pt spectrum for this rangeis relatively featureless. There is the possibility that the Pt spectrum is not of highenough quality to compare features. Further spectroscopy measurements on Ptterraces will be needed to investigate the possibility.59Figure 4.8: Plotted spectra from the center of a spearhead defect (dark purple)as well as it’s two lobes (orange and blue) compared with the pristinebackground shown in gray. In the positive bias range the lobes are notsuppressed. In the negative bias range the two lobes show a higherLDOS than both the center of the defect and the pristine spectrum.Figure 4.9: (a) Linear plot of the spearhead center, spearhead lobe, and Ptterrace spectra. (b) Log plot of plot (a) taken from -500 mV to +500mV. If any similar features exist in the Pt spectrum, noise overpowersthem.60Figure 4.10: A set of three paired STM images of the same spearhead defectstaken at various biases. Second row is a replica of the first row exceptfor a red circle around the Pt sites of interest. Columns (b) and (c) showthe defects imaged at one bias overlayed with theVbias =−400mV scanto better show the atomic resolution. (a) Pair of STM images of thespearhead defect with a lattice overlay. (b) and (c) suggests a Pt atomresides at the center of the defect for both +400mV and +1.0V .4.2.2 Spearhead lattice overlayFigure 4.10 shows lattice overlays placed on top of a spearhead defect for each biasshown in Figure 4.6. The darker spots of the -400 mV scan were used as a guide forthe Pt atoms, similar to Figure 3.2 in Chapter 3. The defect appears as a large brightuneven circle at a negative bias and starts to show some geometric, albeit faded,features at more positive biases. Columns (b) and (c) have the defects cropped outat their respective biases and placed over the -400 mV scan due to the fact thatthe positive biases showed zero atomic resolution for overlay placement, as canbe seen in Figure 4.6. With its varied spectra and topographic shape when pairedwith a lattice overlay, the Pt site is a possible culprit for this defect. However thecurrent data can only provide a minor suggestion of where to start certain density61functional theory (DFT) calculations and further investigations.4.3 Crescent defectContrary to the last two defects, the crescent defect appeared frequently throughoutscanning, and more so towards the end of this experimental run. It often appearedin clusters or not at all.4.3.1 Crescent topography and spectroscopyFigure 4.11: Two scans of separate clusters of crescent defects. (left) Groupof crescent defects scanned at a voltage bias of -400 mV. (right) AnSTM scan of another cluster of crescent defects scanned at +400 mV.Figure 4.11 and Figure 4.12 showcase crescent defects appearing in four dif-ferent orientations total. The +800 mV scan shows the defects as three separateholes with bright lobes offsetting the symmetry of the darker spots from four-foldto almost two-fold in the -400 mV and +400 mV scans. The defect is not quite twofold in symmetry either, as the lobes appear to be weighted more on one side (mostnoticeable in Figure 4.16). While the left and top defects in Figure 4.12 have ori-entations that seem to align with the Pt crystal lattice underneath, the right crescentdefect is not quite a 90o rotation from the other two and is not oriented 90o fromthe Pt lattice underneath. Instead the orientation is similar to how the Sn1 latticesits on top of the Pt lattice.62Figure 4.12: Two STM images of three crescent defects and an artifact inthe bottom center. (left) STM image of crescent defects taken at -400mV in three different orientations. (right) Same STM image of threecrescent defects plus artifact taken at +800 mV.The spectra of the crescent defects mostly matches the Sn1 DOS. Spectra takenon the dark circles show a 60 mV shift to the left of the first peak as seen in Fig-ure 4.13 and Figure 4.14. The two higher valued peaks, however, stay aligned withthe background spectrum. Only the initial +315 mV peak is broadened and shiftedto the left. The brighter lobes of these defects also match the background spectrum.Only the spectra on the darker circles experienced an energy shift as illustrated inFigure 4.14.4.3.2 Crescent lattice overlayInitial lattice overlays on these defects suggested a Sn atom being the likely cul-prit, except for one caveat: the Sn sites with respect to the crescent defects donot stay consistent when the overlays are extended. Figure 4.15 illustrates threelattice overlays that do not align when expanded across the lattice. For a correctlattice placement and good quality scan, the overlays would be expected to orientonto the same lattice site over identical defects as seen in Figure 4.10, Figure 4.21,and upcoming Figure 4.26. The discontinuities highlighted in Figure 4.15 are notresolved if either the Sn or Pt atoms are assumed to be the cause of the crescentdefects. The difficultly faced in aligning the lattice for this type of defect is due63Figure 4.13: (a) STM scan of three crescent defects. (b) dI/dV curves ofthe dark centers of each crescent versus the pristine background takenfrom a grid map. The center of the crescent defects has ≈ ∆ 60 mVLDOS shift to the left of the first peak, while the other two highermagnitude peaks stay aligned with the background.to a lack of clear unsheared imagery on the STM scan and the underlying latticeproving difficult to follow. Furthermore, in Figure 4.16 the symmetry of the latticeis mismatched with the symmetry of the defect. The thinner red arrows show thesymmetry of the proposed defect site within the lattice overlay, while the thickerblue arrows show the symmetry line of the defect shape from the STM scan point-ing to the apex of the bright lobe. Not only do these arrows miss-align completely,they miss-align in different ways with respect to their orientation to each other.The shape of the crescent defects at -400 mV also appears to not have a true mirrorsymmetry through the center. The defects seem to occur at integer values of 90oto each other, which can suggests either a Sn or Pt origin, but sadly most otherconclusions do not have enough evidence to support them.The Sn1 surface is prone to oxidation [85, 103] so it is possible some variationof an Ox or hydroxide molecule has attached itself to exposed Sn atoms and restsoff the surface at random angles, rendering any lattice alignment based off of ori-entation useless. If this defect is a result of a molecule reacting with the surface,scanning on a freshly cleaved sample will bring clarity to its cause. Even so, thisdefect would need clearer, drift free scans to help with lattice placement and/orDFT calculations to give an answer.64Figure 4.14: (a) A linear plot of the bright and dark lobes of the defect com-pared with the Sn1 terrace background. The 60 mV shift is noted bytwo vertical blue lines. (b) A log plot of the same spectra from 0 mVto 800 mV. The log plot clarifies the two higher valued peaks do notundergo any energy shifts, as illuminated by the orange vertical lines.4.4 Butterfly defectThe butterfly defect (as shown in Figure 4.17) is characterized at +400 mV by abright center on top of a darker area with two bright lobes perpendicularly acrossthe center of the defect at positive biases. The butterfly defect has two-fold sym-metry and appears in four orientations, rotated 90o with respect to one another.It varies drastically throughout a range of Vbias, with its bright center overtakingthe defect at lower biases and dimming into black circles at higher biases. Eventhough the Sn terraces do not have four fold symmetry, they still have componentsthat allow for 90o rotations, so this information does not necessarily rule out the Snlayers. The frequency of the butterfly defects did not increase throughout the run65Figure 4.15: STM photo measured at Vbias = -400 mV of several crescentdefects with an attempted overlay. The areas where the overlays refuseto align if a Sn placement is assumed are highlighted in red boxes.of the experiment, which can suggest they are intrinsic to crystal growth.4.4.1 Butterfly topography and spectroscopyThe spectra for the butterfly were also taken via a grid map and is shown in Fig-ure 4.20. The center of each butterfly defect showed a suppressed positive peak ofthe pristine spectrum, similar to the spearhead defect. Unlike the spearhead defect,the negative bias range did not show any new features on either the center of thebutterfly or on the lobes. According to this data, the butterfly defect is simply asuppressed version of the pristine background spectrum of the Sn1 surface.4.4.2 Butterfly lattice overlayA lattice overlay of the first two PtSn4 unit cell layers on top of this defect find acommon Sn site that joins the obtuse and acute angles of the diamonds in the Sn66Figure 4.16: STM photos taken at -400 mV with an attempted lattice overlayassuming a Sn atom is the responsible site for the defect location. (a)STM scan showing the lattice overlay and (b) showing arrows to high-light the orientation discrepancy. The thicker blue arrows slice downthe defects center, starting from the proposed defect site and ending atthe apex of the bright lobe. The thinner red arrows follow the proposedsymmetry of only the lattice. In comparing the angles and order of thearrows of one defect to another, it is clear there is no consistency ineither.Figure 4.17: A set of STM images of the same two butterfly defects at a rangeof differentVbias and all at Iset = 600 pA. From left to right,Vbias = -370mV, +270 mV, +300 mV, and +370 mVlayer with a Pt atom neighboring each side sitting in the dark lobes of the ‘wings”(Figure 4.21). This alignment stays when the lattice is extended across multipledefects. For scans at biases that allow the underlying pristine lattice structure toreveal the Pt lattice, the Sn alignment remains in the same location when the Pt67Figure 4.18: Two larger scans of the same area showing butterfly defects attwo separate biases. (left) 13 butterfly defects scanned at -370 mV.At this negative bias they appear as bright ovals. (right) 14 butterflydefects scanned at +350 mV (the scanning area was shifted downwardsto include a defect originally out of frame). At this positive bias theyappear as dark soft squares with a small bright dot appearing in themiddle. At positive biases (specifically +400 mV) the 90o orientationbecomes easy to track.Figure 4.19: Two scans of the same four butterfly defects, two pairs in differ-ent orientations as well as an artifact at the bottom-right of the cluster.(left) STM scan at Vbias = -320 mV that has an overlay of the Sn1 andPt terraces on top of the image. (right) Same defects scanned at +320mV showcasing the bright and dark lobes of the defect. This bias, al-though only 50 mV lower than the voltage bias used in the left scan ofFigure 4.18, shows a much brighter center.68Figure 4.20: (a STM scan at +320 mV of four butterfly defects spectroscopydata was extracted from. (b) dI/dV of the center of each butterflydefects compared with the pristine surface. (c) dI/dV of each lobe ofone butterfly defect compared to the pristine background.atoms are also aligned.As previously mentioned with the crescent defects, the Sn layers are prone tooxidation. Therefore there is reason to believe there is an Ox or hydroxide adsorbateeither causing the butterfly defects or being drawn to an already existing defect[85, 103]. The butterfly defects did not increase in density over the course ofthe experiment, unlike the crescent and the croissant defect (discussed next). Thebutterfly defect spectrum also represented a suppressed version of the pristine Sn1spectrum, which can indicate an insulating adsorbate dampening the most intenseparts of the spectrum. If the trend of certain defects increasing in frequency overtime is a feature of adsorbates adhering to the surface rather than coincidence ofscanning areas, it could imply that adsorbates responsible for the butterfly defect69Figure 4.21: Three photos of a lattice overlay on top of the butterfly defect atthree separate biases. (a) Two butterfly defects with a lattice overlayextended to cover each defect. The same Sn site falls on the samespot for both defects. (b) Lattice overlay on a butterfly defect alignedwith the Pt spots in the background. The same Sn lattice site sits inthe same area of the defect as proposed in scan (a). (c) Same latticeoverlay placed on top of a scan of the defect at a Vbias of +370 mV.do not bond to a pristine Sn1 surface. But rather, these adsorbate adhere to intrinsicdefects that already existed. DFT calculations of different adsorbate additions willhelp narrow down the cause of this defect.4.5 Croissant defectThe defect that appeared the most often is the croissant defect. The croissant defectis noted by a curved crescent like shape (it was unfortunately discovered after theoriginal crescent defect already received its name. Their differences can be seen inFigure 4.24) that occurs at intervals of 90o at negative biases. At positive biases itregisters as a dark solid circle, as seen in Figure 4.24 and Figure 4.22.704.5.1 Croissant topography and spectroscopyzFigure 4.22: Three different STM images of the croissant defect. The firsttwo on the left were taken with a Vbias = -400 mV while the last oneon the right at +800 mV. The two scans at the negative bias show thedefects taking a croissant like curvature shape while the ones in thepositive bias assume a dark oblong shape.This a peculiar defect, as it did not appear in any capacity in the first fewweeks of scanning. It was first noticed after performing field emission (describedin Chapter 2) on the gold coin surface that neighbors the PtSn4 sample by abouta centimeter or two. A few weeks later field emission was repeated on gold coin,and when the tip returned to scanning on PtSn4, the density increased drastically,as portrayed in Figure 4.25. This observation, although drastic, is not sufficient toconfirm that field emission is responsible for the increase in density of the croissantdefect. The probability of the STM tip returning to the same area it was scanningbefore is slim to none. It is expected that one area of an STM sample will presentdifferently than an area a few millimeters away. A second experimental run on anewly cleaved sample will be able to confirm if the croissants are an artifact offield emission, just intrinsic to this specific sample, or intrinsic to the PtSn4 crystalstructure itself.The spectroscopy data of the croissant defect was difficult to acquire for rea-sons examined in Chapter 5. Point spectroscopy was obtained on the croissantdefect as well as a mysterious dot that appeared next to the defect. This will bediscussed in detail in Chapter 5.71Figure 4.23: (a) A pair of STM images of the croissant and butterfly defecttaken at -400 mV and +400 mV from left to right. The croissantsdefects are circled. (b) A pair of STM images of the croissant andbutterfly defect taken at a different location and point in time comparedto set (a) where Vbias = -400 mV and +400 mV respectively.Figure 4.24: A larger topographic scan with Vbias = -400 mV illustrating sev-eral croissants (top right quadrant) as well as crescent defects (bottomright quadrant). An artifact can be seen in the lower left quadrant.72Figure 4.25: A large 50 nm2 image of many croissant defects taken towardsthe end of the experimental run scanned at Vbias = -400 mV.4.5.2 Croissant lattice overlayIn Figure 4.26 the first two layers of the PtSn4 lattice are overlayed multiple timeson top of an STM scan with croissants. The middle corner of every croissant de-fect, i.e. the top arc of the croissant, aligns to same lattice site, where the angleddiamond shape of Shastry-Sutherland Sn lattice cuts across all the croissants per-pendicularly.This lattice overlay only lines up consistently with the croissant defects forevery half unit cell. This is depicted in detail in Figure 4.27, where each differentcolored circle represents a different site on the Sn1 lattice. For a lattice overlay tobe accurate, the same lattice site must be centered for all the same types of defectsacross an image. This is portrayed in Figure 4.26 and Figure 4.27(a) and (c). Ifan extended overlay across a scan does not consistently align lattice sites overthe same type of defects (recall Figure 4.15), that indicates the overlay placementis incorrect. This is what is shown in Figure 4.27(b) and (d) with the differentcolored circles. Figure 4.27(c) shows the acute angle of the diamond in the Shastry-Sutherland lattice aligning parallel with the apex of the croissant defect, while (d)73Figure 4.26: An STM scan with about a dozen croissant defects. An overlayof the first two PtSn4 unit cell layers are aligned with the atomic resolu-tion seen in this scan to showcase the lattice placements the croissantshave in common. The diamonds are oriented perpendicularly to thecroissant, with the Sn atom at the acute angle of the diamond placed atthe middle corner of the croissant defect.shows the obtuse angle of the Shastry-Sutherland diamond aligning along the apexof the croissant. This latter alignment is not consistent over a wide spread area asshown in image (b).If the Pt atoms in the overlay are shifted a row up or down to align with thenext row of dark spots on the STM images, the croissant defect sites differ in atotal of three separate orientations. This is depicted in Figure 4.27(b) and (d) asblue, orange, and red circles. If this shifted overlay was true, it would topographi-cally result in different shaped defects with different properties as the source of thedefects. Instead they all appear the same geometrically and have the same proper-ties. Therefore images (a) and (c) are the correct overlay placement, since everylattice spot on the croissant peak is consistent as showcased in Figure 4.26 and74Figure 4.28.Figure 4.27: (a) Figure 4.26 with green circles around each croissant, notingmatching lattice sites. (b) Same scan from (a) with the lattice overlayshifted up by one half unit cell and realigned to the Pt in the scan.Circles are color coded to the different types of lattice sites they alignedwith. With this overlay, three different lattice site options exist withinone image, which is not consistent with the defect presentation. (c)and (d) Two sets of the same STM image showing a close up of twocroissant defects with the correct and incorrect overlay respectively.The two acute angles within the Shastry-Sutherland lattice of the Sn1 over-lay align themselves perpendicularly across the apex of the croissant to the innercurved corner. From the data and overlays presented here, determining which ofthese two Sn sites is responsible is inconclusive. DFT calculations are required to75discern the responsible lattice ssite from the two.Figure 4.28: A set of three STM images of croissants. Each croissant hasthe acute angle of the Sn layer sitting perpendicular inside it. The Snatoms sitting in the acute angles of the diamonds are highlighted withlight hued circles.The croissant defect was the most peculiar to observe topographically. As scan-ning was performed on this defect in particular, an interesting phenomenon startedhappening when theVbias magnitude exceeded a certain value, and will be exploredin detail in the next chapter.4.6 Recap of defectsA total of five different defects on the Sn1 layer were scanned and documented onPtSn4. The 4-fold defect’s symmetry strongly suggests it resides in the Pt layer.The 4-fold defect was only seen on two separate occasions throughout the entireexperimental run which makes it the rarest defect. The spearhead defect was alsoa rare find. Lattice overlays on the spearhead defect suggested a Pt source as well,although less convincingly than the 4-fold. Both of these defects are likely to centeroff of a Pt site defect and only appeared a small handful of times. All other defectson the other hand were much more common, and suggest Sn lattice sites, with thecrescent defect remaining unclear. The extreme rarity of the Pt centered defectscould possibly explain a lower resistance avenue of electron transport along the Ptlayer. Given this Pt layer is proving to be resistant to defects, a low intrinsic defectdensity is a probable cause for the high RRR seen with this sample.The crescent defect was the only defect to show a shift of a spectral featurefrom the background spectra but proved inconclusive in finding a responsible lat-76tice site. The butterfly defect had spectra that was a suppressed version of thepristine Sn1 spectrum, with a Sn lattice site being the most likely culprit. Whetherthat site is the home of an adsorbate or an intrinsic defect is unclear. The croissantdefect showed little to no change in spectra compared to the background. A latticeoverlay on top of the croissant defects proved that the defects sit in between thediamonds formed within the Sn Shastry-Sutherland lattice where the length of thediamond intersects the defect perpendicularly. This leaves the acute angles of theSn diamond aligned with both the outer and inner arcs of the defect. Some defectsneed further scanning to better understand them such as the spearhead and crescent.All need DFT calculations to fully rule out/confirm their causes.All of the defects presented in this work were discovered while scanning onthe Sn1 plane. The Sn2 surface was rare, and the Pt surface even more so. Moreextensive scanning is required to find viable surfaces of the Pt and Sn2 terraces.Scanning on different terraces to compare known defects, characterize new ones,and document patterns that arise can help distinguish defect origins and thereforethe electron transport of PtSn4. Table 4.1 outlines suggested scanning biases foreach defect to acquire the best topographic photo that also gives the best contrastfor the pristine Sn1 lattice.Table 4.1: A table showing approximate suggestions of Vbias depending onwhat defects are being scanned. These biases should best show the finerdetails of the defects as well as show the underlying pristine crystal struc-ture. It should be noted that although a Vbias around +300 mV for thebutterfly defect will show its specific detailing, the best the atomic reso-lution will be very difficult to acquire at this bias.Defects in Scan Proposed Vbias4-fold ≈ less than -400 mVSpearhead ≈ greater than +800 mVCrescent ≈ less than -400 mVButterfly ≈ -400 mV or ≈ +300 mVCroissant ≈ -400 mV77Chapter 5Analysis of rotating defectsFigure 5.1: Two consecutive STM scans of the same defects taken a few min-utes apart, showing that the top left and bottom right defects have movedvia rotation.The croissant defect has frequently been found to rotate as a result of the tipinteracting with the defect. As seen in Figure 5.1, these defects have been observedto rotate to any of the 4 orientations observed for them, as well as translating acrossthe surface using the rotations as a means of transport.78Figure 5.2: A set of STM images read left to right with Vbias = −1.0V andIset = 600pA demonstrating the rotations of the croissant defects. Eachdefect in every scan presented has a white outline of the original posi-tions of the defects to highlight the rotations and travel during succeed-ing scans.Figure 5.3: A series of four consecutive STM scans (read left to right) of thesame scanning area and defects taken at a voltage bias of -1.0 V and Iset= 600 pA. Similar to Figure 5.2, the defects in the first scan on the leftare outlined in white. Said outline is overlayed on additional scans todetail the movement of the croissants.5.1 The Rotating DefectFigure 5.2 through Figure 5.6 portray rotations of the croissant defect at both apositive and negativeVbias. A majority of the defects in Figure 5.6 appear disrupted.This is due to the fact that a croissant sometimes rotates as the tip scans over it,which can also be seen in Figure 5.7. An STM records the information of a surfaceline by line as it scans. Each line takes a finite amount of time to complete. If thematerial underwent a change within this finite amount of time, the resultant scanmay not be the most up to date representation of the current state of the material.The defects in Figure 5.6 and Figure 5.7 show defects that rotated during mid scandue to tip interaction. This “live” rotation can appear as half of a defect if it rotatesbehind the scanning path, or elongated if it rotates in front of it.Extensive scanning and tip manipulation were performed in an attempt to con-79Figure 5.4: Two consecutive scans of the same area showing both croissantand crescent defects. (left) STM image taken at -400 mV. Five defectsare circled in orange. (right) The same five defects are outlined in bluenoting a rotation by 900 in either the clockwise or counterclockwisedirection.trol the direction, trigger, and frequency of the rotations. Scanning direction hadno predictable influence on the travel of the defect. Moving the tip while tun-neling over the defect at angles normal to its various sides also did not result inpredictable rotations or movement. Over the thousands of croissants scanned, thedirection of the rotations and movement appears random. The one thing that re-mained predictable was the range of Vbias used that would initiate the rotations.Further scanning revealed that this rotating behavior was consistent while imagingdefects at a high magnitude Vbias, either positive or negative. Scanning at highervoltage magnitudes would guarantee rotations, with the favorite Vbias being set toeither -1.00 V or +1.00 V. -400 mV remained a trustworthy voltage bias to imagethe defects without triggering any rotations.In order to discern if the rotations were a result of exciting a specific state ata particular Vbias value or were an effect of the tip’s electric field influence on thesurface, several hundred scans were performed on croissants where the |Vbias| wasvaried from 400 mV upwards to find the lowest bias that would cause a rotation.The lowest Vbias magnitude that would cause a rotation was 690 mV, as depictedin Figure 5.8. The threshold was symmetric and independent of the sign of thevoltage bias; a negative bias beyond -690 mV and a positive bias beyond +690 mV80Figure 5.5: A series of 15 STM images taken consecutively where each crois-sant defect rotates at least once. The first image was scanned with aVbias= -400 mV while the other 14 were scanned at -1.0 mV. All scans usedan Iset = 600 pA. After the first scan at -400 mV, each scan took 78.8seconds to complete before the next once was immediately started. Awhite outline of the original defect locations is overlayed on each imageto illustrate the movement.both causes rotations. Frequency of rotation did decrease as the magnitude of Vbiasdecreased. This fact coupled with the observation that the croissants did not rotate100% of the time leaves behind a small chance that the croissants can rotate atbiases below 690 mV. In the conditions of this experiment, any rotations below amagnitude of 690 mV were unlikely but cannot be ruled out as impossible.In addition to the steady increase of rotation frequency as Vbias increases, thesymmetry of the range strongly suggests that the rotations are caused by the elec-tric field interactions between the tip and the sample. Rotations as an effect of aspecific energy state being excited would most likely portray an asymmetricalVbiasrange of rotations. A rotation inducing negative voltage bias that did not causerotations on the positive side of the spectrum (and vice versa) was never found. AsVbias increases, the electric field becomes stronger and more likely to influence thesurface which aligns with the increased frequency of rotations seen at higher Vbias.81Figure 5.6: A series of 9 STM images of the croissant defect. The first 8images were taken consecutively at Vbias = +800 mV with 15.9 secondsin between each scan. The last scan was taken at -400 mV to betterdetermine the angle of rotation. Elongated defects as well as crisp linescutting defects through the centers indicate rotations mid scan.Figure 5.7: (a) A series of 6 STM scans taken over one defect, increasing themagnitude of the negative Vbias by 100 mV each scan. A rotation wasfinally seen at -900 mV. (b) Consecutive scans 4.9 s apart all using Vbias= -900 mV, showcasing rotations as well as the third and fifth rotatingmid scan.82Figure 5.8: A visual representation showing that rotations were not witnessedunder |Vbias| = 690 mV. Values above |Vbias| = 1 V caused rotations,depicted by the ellipses on the line graph.The electric field that results from the tip-sample interaction is very dependenton the shape and size of the tip, as detailed in Chapter 2. Meaning the observedrotation limit found with this STM tip may not be the same for a different tip orafter a severe tip event. Further scanning with a tip in a different state will helpconfirm whether or not the electric field influence is responsible for the croissantrotations.5.2 Peculiar related phenomenaIn addition to the rotations, the croissants were observed performing other inter-esting phenomena across the experimental run. After the mode of rotations wasdependably triggered, experiments were performed on areas where croissant de-fects dominated the scanning space. One of the techniques was as follows: animage was acquired at -400 mV, then the tip was withdrawn, brought to the centerof the scanning area, set to -1.0 mV, then tunneled at Iset = 600 pA for 60 seconds.After 60 seconds the tip was withdrawn, set back to Vbias = -400 mV, then anotherimage was scanned. -400 mV was chosen as it was the most stable voltage biaswhere no rotations at the time had been observed, while also showing atomic res-olution. The goal of this was to infer a radius of influence the electric field at thetunneling junction had on the croissants. An unexpected result of this experimentis visible in Figure 5.9.The two croissant defects highlighted in the orange circles in Figure 5.9 orig-inally presented very close together, with the bottom left one rotated by an differ-ence of 90o. The tip tunneling in the center of the scanning area for 60 seconds83Figure 5.9: (a) Initial scan showing two croissants perpendicular to eachother within the orange circle. (b) Secondary scan showing the bottomleft defect of the highlighted pair had rotated by 900. (c) The consecu-tive scan taken right after the tip tunneled at -1 V in the center of the im-age for 60 seconds. Circle shows where the two defects were expectedto be and are not. (insets) Zoomed in images of the croissant defectsof interest. All images and stationary tip tunneling were scanned/per-formed at Iset = 600 pA.caused the aforementioned croissant defect to rotate by 90o causing the two de-fects to now mirror each other (see Figure 5.9(b)). The tip was then brought to thecenter and tunneled at -1.0 mV, after which the last scan revealed the two defectshad seemingly canceled each other out and disappeared. Figure 5.10 has circledeach whole croissant defect in the image. If the defects simply moved instead ofdisappearing, the total number of croissants in the area would stay constant acrossthe three scans. Instead, scan (c) has two less croissant defects in total at N = 24compared to (a) and (b) at N = 26. It is possible that the defects have moved to anarea outside of the visible scanning region, but this is argued to be highly unlikely,as rotations were not observed to be that drastic over one period of interacting withthe tip. Other scans recorded during this style of experiment (center tunneling)also did not reveal any long traveled defects even if the tip was left tunneling in thecenter at -1 V for an hour. Figure 5.11 shows a secondary instance of a croissantcancellation under the same conditions.In contrast to two croissants disappearing via rotations, they have also beenobserved appearing via what seem to be the rotation of another croissant as seen inFigure 5.12. In attempt to influence the direction of rotation, the tip was draggedin various ways across croissant defects while scanning. An image was first was84Figure 5.10: The base figures of Figure 5.9 with all full croissant defectscounted and circled. (a) 26 defects are accounted for. (b) 26 defectsare accounted for after the one rotation from the defect of interest andsome rotations of neighboring defects. (c) 24 defects are accountedfor showing that if the two defects did not “undefect” themselves, theymust have traveled significantly out of range. All scans had parametersof Vbias = -400 mV and Iset = 600 pA.Figure 5.11: Another instance where two croissant defects were recorded an-nihilating each other under the same experimental process denoted inFigure 5.9. All scans had parameters of Vbias = -400 mV and Iset = 600pA.scanned at the presumed safe -400 mV bias, tip was withdrawn, then brought nor-mal to the croissant. The Vbias and/or Iset were changed to different values, thetip was brought back to tunneling then moved straight across the croissant. Thetip was immediately withdrawn and reverted back to the stable settings, and thenre-scanned to check for movement. Influencing the rotational direction proved dif-ficult and unpredictable, but it was during this testing that the two croissants in85Figure 5.12 appeared, facing the same orientation as the tip movement.These scans cover a smaller area than Figure 5.9, so it is still necessary to enter-tain the possibility that these new defects were originally out of frame and rotatedinto the image. However, this is unlikely since the tip interaction with the surfacein Figure 5.12 is weaker than both types of interaction that caused the behavior inFigure 5.9, as well as normal tip-sample scanning interactions. In addition, rota-tions covering distances more than two to three lattice sites have not been observed.While croissants suddenly traveling into frame (and not materializing on the spot)is unlikely, it is still a possibility and must be considered until future larger scansand DFT calculations can rule out any long distance defect traveling.Figure 5.12: A set of three consecutive STM images of several croissant de-fects. In between each scan the STM tip (while tunneling) was pur-posefully moved over the bottom right defect in the direction of thearrow in an attempt to influence rotation. (a) STM image of four crois-sant defects where the tip moved a short distance perpendicularly overthe defect. (b) STM image showing that three of the four defects ro-tated under the influence of the tip movement described in image (a).The technique was repeated, dragging the tip now parallel to the de-fect. (c) The consecutive scan at the presumed safe -400 mV voltagebias, revealing two new defects shown in the circles.On a few uncommon occasions, some croissants left behind artifacts after rotat-ing past certain lattice sites. These appeared as brighter, singular spots on a brightlattice site. The one shown in Figure 5.13 was stable enough to allow some spec-troscopy measurements. After a few STS measurements it grew topographicallyfainter in one discrete step and then eventually disappeared.86As mentioned at the end of Chapter 4, the spectroscopy measurements per-formed on the croissant proved difficult to acquire. The croissant’s tendency torotate at magnitudes above 690 mV made spectroscopic measurements untrust-worthy. The spectra in Figure 5.13 were acquired by taking scans at -400 mV inbetween each spectrum collection to confirm if a rotation occurred. If a rotation didoccur, the spectrum was not used. Unfortunately since croissants move in discreterotations/translations, it is possible a croissant rotated out and then back into placeduring a spectroscopic measurement. This would go undetectable from scanningat a safe voltage bias before and after to confirm positioning. So while some ofthe spectra shown in Figure 5.13 has a slight chance of not fully portraying datafrom the croissants (the orange and blue dots at the most bottom part of the insetin Figure 5.13), the spectra from the random bright dot as well as the backgroundis deemed trustworthy.Figure 5.13: A plot of four different spectra on or around a croissant defectwith insets of a small scan over a singular croissant and the mysteriousdot taken at Vbias = -400 mV. The brightest part of the defect is shownin orange and the dark area inside the defect is shown in blue. Therandom dot is shown in dark purple while the background is shown ingray.While the random singular dot seemed to have a slightly suppressed dI/dVwhen compared to the pristine background in Figure 5.13, other parts on andaround the defect showed a depression of features and no energy shifts. The spectraof and around both the croissant defect and the random dot closely resembled theSn1 spectrum, and no obvious spectral shifts or changes in features were found.87Figure 5.14: Cartoon representations of a proposed theory behind the crois-sant rotations. (a) A demonstration of a vacancy underneath a dis-lodged Sn atom shifting to the rightmost nearest neighbor, causing arotation. (b) A demonstration of a vacancy-Sn pair shifting to the up-per nearest neighbor causing a rotation.5.3 Proposed theory behind rotationsThe most that STM imaging can confirm is the superficial crystal structure andlattice sites responsible for certain defects. Verifying the mechanisms responsiblefor a defects origin and behavior (such as rotations) requires further analysis andDFT calculations simulating the surface. With that being said, the current standinghypothesis is a Sn atom is dislocated out of its normal site and rests slightly abovethe terrace, sticking out of the lattice while still bonded to two other Sn atoms via88the acute angle in the diamond shape within the Sn lattice. Due to the symmetry ofthe crystal lattice, every nearest neighbor is a Sn atom that has an acute bond angleattached to it at some 90o interval. The vacancy paired with the disjointed Sn atomcan hop to one of the nearest neighbors, dislocate a new Sn atom by breaking allbonds except for the acute angled bonds, resulting in a rotation. Whether or not thedislocated Sn atom fills in the vacancy first causing a neighboring Sn to pop out, orif a neighboring Sn in the lattice fills the vacancy causing the dislodged Sn to moveover the new vacancy remains unclear. The general outcome remains the same; adislocated Sn atom has moved to hover over a vacancy on a different lattice site.The mechanisms of this effect are depicted in Figure 5.14 for two separate vacancymovements and the general dislocation structure is shown in Figure 5.15. Thecroissant defects have been well documented traveling around the lattice via theserotations which can happen through a series of several rotation variations.Figure 5.15: A set of images displaying a lattice overlay and dislocated Snatoms. (a) the STM image used with aVbias = -1.0 V and Iset = 600 pA.(b) same image with the lattice overlay, showing the Sn atoms that are“out of socket.” These are represented by the larger light purple dotson the image. (c) the overlay of the first Sn and Pt layer without theSTM image for clarity.Figure 4.28 in the previous chapter shows three STM images taken consecu-tively at biases that cause rotations. Two Sn atoms on each defect are highlighted.As mentioned in Chapter 4, it is unclear which of the two Sn atoms in the acuteangles of the diamond are responsible for the dislocated defect in this hypothesis.As for now it is assumed the dislocated Sn atom is the one belonging to the acuteangle on the inside of the defect’s curvature. This orientation makes the healing of89the lattice seen in Figure 5.16 more plausible.Figure 5.16: (a) Close up of the STM image where two croissants appearedto merge and heal the lattice with an overlay of the Sn and Pt layer,as well as showing the dislocated Sn defects. (b) Same scanning areaafter the defects disappeared, showing an unperturbed crystal latticeoverlay on top.This hypothesis uses the suggestion of a dislodged Sn atom as opposed to sim-ply a lone vacancy due to the disappearing/appearing phenomena seen in Figure 5.9and Figure 5.12. Two vacancies merging together would create a bigger hole, notheal the crystal lattice, as we see in Figure 5.9 and Figure 5.11 introduced in theprevious section. Furthermore the annihilations witnessed, although few, have onlyhappened in pairs. With the inner Sn atom chosen as the culprit, the suspectedSn atoms in the annihilation scenario directly face one another, possibly creatingenough interference to “pop” them back into place. Figure 5.14 visualizes thisphenomena and shows the resultant rotation of 90o. Again, further analysis will berequired to confirm these hypotheses.Rotations and appearances of both adsorbates and quasiparticles have been ob-served and documented via STM in literature starting over 30 years ago at varyingdegrees of control [104–108]. Most documentation discusses experimentally de-posited adsorbates moving in environments at temperatures on the range of 8 K to100 K [106, 109, 110]. The croissant defect in this thesis, on the other hand, wasscanned at liquid helium temperatures and is intrinsic to the experiment — whetheror not the moleucle in question is native to the crystal structure or an unintentional90adsorbate from the environment remains unclear. The observations of two crois-sants merging to heal the lattice discourages the possibility of an adsorbate-baseddefect. Although an adsorbate source is not completely ruled out, this lattice heal-ing suggests the possibility that the croissant defect is intrinsic to this material, andamong any nmaterial is a rare occurrence of atomic manipulation within a pristinecrystal lattice.91Chapter 6ConclusionThis work documents the first extensive attempt to explore the topological semi-metal PtSn4 via STM and STS. While the three different terraces and correlatingspectrum were identified, confirming defects proved more challenging. The goalof this thesis was to provide detailed documentation on terraces and defects thatappeared, as well as explore possible explanations of the high RRR seen in PtSn4and to what extent a low defect density was responsible.Chapter 1 discussed a brief and concise idea of topology in the lens of con-densed matter physics. The material in question was then introduced to be apromising candidate for STM with its topological surface states, layered struc-ture, and a promising cleaving plane. Chapter 2 reviewed the theory behind STM.STM would not be possible without quantum tunneling, and due to the fermionicnature of electrons, STS allows for the probing of their energy states. Throughclever assumptions of the tunneling matrix at the tunneling junction between tipand sample as well as picking a tip with a monotonous DOS, the DOS of the ma-terial becomes analogous to the dI/dV curve acquired by sweeping the bias whilethe tip is tunneling. The intertwined relationship between the DOS influence andthe topography of scanning was reviewed in detail. From the derivation of the tun-neling equation, it is noted that the dI/dV is proportional to the DOS, which meansthe integral of the DOS is proportional to the current. The raw height of the sampleto the tip is directly dependent on the current. Meaning two different surfaces withdifferent values of integrated DOS from 0 to a certain Vbias have an effect on the92height of the sample the data shows versus what is real. This effect became evidentin Chapter 3.In Chapter 3, the three main terraces (Sn1, Pt, and Sn2) are confirmed using amixture of known step edge heights as well as the three separate spectra observed.By taking histograms of the z profile data of scans with numerous step edges andcoupling that with the known spectra of certain terraces, layers of atoms withinthe crystal lattice were able to be aligned. Keeping in mind the DOS influence asoutlined in Chapter 2, all but one terrace step was accounted for. As a result, allthree terraces could be matched with three different spectra.Chapter 4 outlined the five different defects found while scanning on this sam-ple of PtSn4. From the most rare to the ones that littered the surface: the 4-folddefect, the spearhead defect, the crescent, the butterfly, and last but certainly notleast, the croissant. All suggestions for the defects are tentative, with some hold-ing stronger corroborations to their origins than others. The 4-fold defect showedminimal spectral changes besides a flattening of the first trough in the spectrumtaken from its center. Despite the ambiguity of the spectra, the topographic lobesseen of the 4-fold defect align with some of defect’s nearest Pt neighbors whenthe Sn1 and Pt lattice were overlayed on top. The Pt lattice is the only layer inthe PtSn4 unit cell with 4-fold symmetry, which strongly indicates this is either aPt site substitution or vacancy. The spearhead defects showed suppressed peaks inthe spectra when compared to the pristine background spectra, while the lobes ofthe defect showed an increase of states in the negative bias range. The crescentdefect spectra showed a slight energy shift in the dI/dV , but any lattice overlayswere inconclusive. The butterfly defect also showed a suppressed spectroscopicpeak, with overlays pointing to a Sn site being the responsible culprit. The poten-tial lattice sites responsible for the croissant defect have been narrowed down totwo candidates. In Chapter 5, the rotational behavior of the croissants was docu-mented, and a theory was proposed to explain the causes of the croissant rotationsand travel, as well as the witnessed healing of the lattice and sudden appearance ofsaid defects. More extensive scans allowing for crisper atomic resolution will helpaid in confirming the origins of these defects, specifically the spearheads and cres-cents. All defects except the crescent have potential lattice sites proposed, whichDFT calculations are needed to confirm. Simulations will also help discern which93defects are structural anomalies in the material that could interfere with its RRRand which are adsorbates.The rarity of the 4-fold defect paired with its probable existence in the Pt layersof PtSn4 reveals the possibility of a conduction channel primarily involving the Ptlayers, which has high mobility due to very low defect density in that layer. Thiscould generate the very high RRR seen in this material.The Sn surface of PtSn4 is prone to oxidation although this has negligible ef-fects on the topological states of the valence band [103, 111]. While oxidation orother possible adsorbates are most likely not responsible for the 4-fold defect, andcannot be ruled out as a probable cause for the croissant defect, it is a probablecause for the remaining three. Further scanning on a sample with lower RRR canhelp deduce the differences between intrinsic defects, adsorbates, and absorbatespossibly drawn to specific defects.6.1 Future directionsAt the time of writing, the PtSn4 sample used in this thesis has been recleaved fora second attempt at scanning. Another fast cooled XMR PtSn4 sample has beengrown with a significantly lower RRR with the intention of also performing exten-sive STM and STS studies on its surface. Comparing the various defect densitieson this fast cooled sample compared to what was observed on the sample docu-mented in this work will help determine which defects are intrinsic to the latticeversus adsorbates. DFT calculations still need to be performed on various potentialsurface state configurations to confirm.Multiple grid maps have been acquired for all the defects documented in thiswork. These will be used for QPI analysis which explores the most common scat-tering vectors of electrons. QPI is a powerful tool that extrapolates momentumspace information from real space data and allows for the direct study of scatter-ing events in the surface state of materials. Quasiparticles scatter off of defects ina material, creating standing waves which can be analyzed via Fourier-transformscanning tunneling spectroscopy (FT-STS) [102].In the future, scanning on other materials in the family of PtSn4 (IrSn4 andAuSn4) will help gather a deeper understanding of topological effects on electron94carrier mobility. Contrasting to PtSn4, AuSn4 exhibits a weak MR in addition tobeing superconducting at Tc ≈ 2.4 K. 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Thesis/Dissertation
eng
Physics
Vancouver : University of British Columbia Library
Attribution-NonCommercial-NoDerivatives 4.0 International
Graduate
Bonn, Douglas
Defect and terrace characterization of PtSn₄ using scanning tunneling microscopy and spectroscopy
Text