Heavy-Tailed Hall Conductivity Fluctuations in Quantum Hall Transitions
Mesoscale and Nanoscale Physics
2026-01-01 v1
Abstract
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 --, 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.
Keywords
Cite
@article{arxiv.2512.24021,
title = {Heavy-Tailed Hall Conductivity Fluctuations in Quantum Hall Transitions},
author = {Emuna Rimon and Eytan Grosfeld and Yevgeny Bar Lev},
journal= {arXiv preprint arXiv:2512.24021},
year = {2026}
}