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The quantum hall effect and bulk-edge correspondence on lattice systems Furlotte, Justin
Abstract
In this thesis, we investigate the integer quantum Hall effect (IQHE). Discovered in 1980 by Nobel laureate Klaus von Klitzing, the IQHE is a phenomenon in which the conductivity of a 2-dimensional electron gas is quantized in exact integer multiples of q²/h when subjected to a strong magnetic field at very low temperatures. In particular, we provide a rigorous theoretical description of a phenomenon known as bulk-edge correspondence, wherein the value of the Hall conductivity is unaffected by whether or not one considers a system with an edge or a bulk (i.e. edgeless) system. This is accomplished in two settings. First, we ignore interactions between electrons, and then proceed to the more challenging interacting setting.
Item Metadata
| Title |
The quantum hall effect and bulk-edge correspondence on lattice systems
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| Creator | |
| Supervisor | |
| Publisher |
University of British Columbia
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| Date Issued |
2022
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| Description |
In this thesis, we investigate the integer quantum Hall effect (IQHE). Discovered in 1980 by Nobel laureate Klaus von Klitzing, the IQHE is a phenomenon in which the conductivity of a 2-dimensional electron gas is quantized in exact integer multiples of q²/h when subjected to a strong magnetic field at very low temperatures.
In particular, we provide a rigorous theoretical description of a phenomenon known as bulk-edge correspondence, wherein the value of the Hall conductivity is unaffected by whether or not one considers a system with an edge or a bulk (i.e. edgeless) system. This is accomplished in two settings. First, we ignore interactions between electrons, and then proceed to the more challenging interacting setting.
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| Genre | |
| Type | |
| Language |
eng
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| Date Available |
2022-08-23
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| Provider |
Vancouver : University of British Columbia Library
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| Rights |
Attribution-NonCommercial-NoDerivatives 4.0 International
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| DOI |
10.14288/1.0417482
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| URI | |
| Degree | |
| Program | |
| Affiliation | |
| Degree Grantor |
University of British Columbia
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| Graduation Date |
2022-11
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| Campus | |
| Scholarly Level |
Graduate
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| Rights URI | |
| Aggregated Source Repository |
DSpace
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Rights
Attribution-NonCommercial-NoDerivatives 4.0 International