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Child, Timothy James

University of British Columbia

Direct measurements of entropy in mesoscopic systems offer a promising pathway to explore a wide range of exotic quantum phenomena, especially those that prove challenging to investigate through conventional transport metrics. While entropy evaluations have traditionally depended on bulk properties like heat capacity – readily measurable in macroscopic systems – these approaches become ineffective at a mesoscopic scale where such properties are vanishingly small. For mesoscopic systems, a fundamentally different approach is required. This thesis introduces a novel entropy measurement protocol, founded on a Maxwell relation, that is universal for arbitrary mesoscopic circuits. It is developed, tested, and applied to systems of increasing complexity within two-dimensional electron gases (2DEGs) hosted in GaAs/AlGaAs heterostructures. The central focus of the research is the development and validation of a universal entropy measurement protocol tailored for mesoscopic systems. This method is first demonstrated on a quantum dot weakly coupled to a thermal reservoir, affirming its effectiveness and showcasing the capability to continually assess entropy change throughout a charge transition – a marked advancement over the foundational approach that inspired this work. The protocol is next applied to a double quantum dot system, illustrating its aptitude to measure non-local entropy via capacitive coupling. The protocol’s universality is highlighted through measurements of a quantum dot hybridized with an electron reservoir, where density-matrix numerical renormalization group simulations align with experimental results up to intermediate coupling strengths. A notable divergence between theory and experiment emerges for stronger couplings, particularly where Kondo correlations are anticipated (in the mixed valence regime), raising intriguing questions yet to be answered. Lastly, preliminary measurements from a newly configured device that facilitates operation in the Kondo regime are discussed. The findings suggest spin suppression in the system, potentially marking the first observation of the entropic effect of a persistent Kondo-correlated singlet state. This research establishes a fundamentally new technique with wide applicability, reaching beyond GaAs/AlGaAs 2DEGs to include other 2D mesoscopic systems such as layered graphene structures. As the field of quantum entropy measurement advances, this work sets a robust platform for future studies targeting a myriad of exotic quantum systems.

Text

2024-03-19

Attribution-NonCommercial-NoDerivatives 4.0 International

http://hdl.handle.net/2429/87596

Physics

University of British Columbia

UBCV

http://creativecommons.org/licenses/by-nc-nd/4.0/