LOCALIZATION IN A RANDOM MAGNETIC-FIELD - THE SEMICLASSICAL LIMIT
We study the two-dimensional electron gas in the presence of a random perpendicular magnetic field. We examine, in particular, the limit in which the correlation length of the random field is large compared to the typical magnetic length. In this limit, a semiclassical approach can be used to unders...
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| Format: | Journal article |
| Language: | English |
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1994
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| _version_ | 1797103976225701888 |
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| author | Lee, D Chalker, J Ko, D |
| author_facet | Lee, D Chalker, J Ko, D |
| author_sort | Lee, D |
| collection | OXFORD |
| description | We study the two-dimensional electron gas in the presence of a random perpendicular magnetic field. We examine, in particular, the limit in which the correlation length of the random field is large compared to the typical magnetic length. In this limit, a semiclassical approach can be used to understand a large part of the energy spectrum. To investigate localization, we introduce a simplified model, in which electrons propagate coherently on a random network derived from the classical trajectories. The same network model (with different parameters) also represents electron motion in a uniform magnetic field and a random scalar potential, in a spin-degenerate Landau level. Requiring that the global phase diagram of our model be consistent with Khmelnitskii's scaling flow for the quantum Hall effect, we argue that all electron states in a random magnetic field are localized in the semiclassical limit. We present the results of numerical simulations of the model in support of this conclusion. © 1994 The American Physical Society. |
| first_indexed | 2024-03-07T06:27:42Z |
| format | Journal article |
| id | oxford-uuid:f4e2c2c2-e093-4338-968e-f5231767e0c6 |
| institution | University of Oxford |
| language | English |
| last_indexed | 2024-03-07T06:27:42Z |
| publishDate | 1994 |
| record_format | dspace |
| spelling | oxford-uuid:f4e2c2c2-e093-4338-968e-f5231767e0c62022-03-27T12:23:06ZLOCALIZATION IN A RANDOM MAGNETIC-FIELD - THE SEMICLASSICAL LIMITJournal articlehttp://purl.org/coar/resource_type/c_dcae04bcuuid:f4e2c2c2-e093-4338-968e-f5231767e0c6EnglishSymplectic Elements at Oxford1994Lee, DChalker, JKo, DWe study the two-dimensional electron gas in the presence of a random perpendicular magnetic field. We examine, in particular, the limit in which the correlation length of the random field is large compared to the typical magnetic length. In this limit, a semiclassical approach can be used to understand a large part of the energy spectrum. To investigate localization, we introduce a simplified model, in which electrons propagate coherently on a random network derived from the classical trajectories. The same network model (with different parameters) also represents electron motion in a uniform magnetic field and a random scalar potential, in a spin-degenerate Landau level. Requiring that the global phase diagram of our model be consistent with Khmelnitskii's scaling flow for the quantum Hall effect, we argue that all electron states in a random magnetic field are localized in the semiclassical limit. We present the results of numerical simulations of the model in support of this conclusion. © 1994 The American Physical Society. |
| spellingShingle | Lee, D Chalker, J Ko, D LOCALIZATION IN A RANDOM MAGNETIC-FIELD - THE SEMICLASSICAL LIMIT |
| title | LOCALIZATION IN A RANDOM MAGNETIC-FIELD - THE SEMICLASSICAL LIMIT |
| title_full | LOCALIZATION IN A RANDOM MAGNETIC-FIELD - THE SEMICLASSICAL LIMIT |
| title_fullStr | LOCALIZATION IN A RANDOM MAGNETIC-FIELD - THE SEMICLASSICAL LIMIT |
| title_full_unstemmed | LOCALIZATION IN A RANDOM MAGNETIC-FIELD - THE SEMICLASSICAL LIMIT |
| title_short | LOCALIZATION IN A RANDOM MAGNETIC-FIELD - THE SEMICLASSICAL LIMIT |
| title_sort | localization in a random magnetic field the semiclassical limit |
| work_keys_str_mv | AT leed localizationinarandommagneticfieldthesemiclassicallimit AT chalkerj localizationinarandommagneticfieldthesemiclassicallimit AT kod localizationinarandommagneticfieldthesemiclassicallimit |