Heavy-Tailed Hall Conductivity Fluctuations in Quantum Hall Transitions

Fuente: arXiv
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Main Authors: Rimon, Emuna, Grosfeld, Eytan, Lev, Yevgeny Bar
Format: Preprint
Published: 2025
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author Rimon, Emuna
Grosfeld, Eytan
Lev, Yevgeny Bar
author_facet Rimon, Emuna
Grosfeld, Eytan
Lev, Yevgeny Bar
contents We study the full distribution of the zero-temperature Hall conductivity in a lattice model of the IQHE using the Kubo formula across disorder realizations. Near the localization-delocalization transition, the conductivity exhibits heavy-tailed fluctuations characterized by a power-law decay with exponent $α\approx 2.3$--$2.5$, indicating a finite mean but a divergent variance. The heavy tail persists across a range of system sizes, correlation lengths of the disorder potential and fillings. Our results demonstrate a breakdown of self-averaging in transport in small, coherent samples near criticality, in agreement with findings in random matrix models of topological indices.
format Preprint
id arxiv_https___arxiv_org_abs_2512_24021
institution arXiv
publishDate 2025
record_format arxiv
spellingShingle Heavy-Tailed Hall Conductivity Fluctuations in Quantum Hall Transitions
Rimon, Emuna
Grosfeld, Eytan
Lev, Yevgeny Bar
Mesoscale and Nanoscale Physics
We study the full distribution of the zero-temperature Hall conductivity in a lattice model of the IQHE using the Kubo formula across disorder realizations. Near the localization-delocalization transition, the conductivity exhibits heavy-tailed fluctuations characterized by a power-law decay with exponent $α\approx 2.3$--$2.5$, indicating a finite mean but a divergent variance. The heavy tail persists across a range of system sizes, correlation lengths of the disorder potential and fillings. Our results demonstrate a breakdown of self-averaging in transport in small, coherent samples near criticality, in agreement with findings in random matrix models of topological indices.
title Heavy-Tailed Hall Conductivity Fluctuations in Quantum Hall Transitions
topic Mesoscale and Nanoscale Physics
url https://arxiv.org/abs/2512.24021