Breakdown of Self-Averaging at Quantum Hall Transitions.

Authors

Emuna Rimon, Eytan Grosfeld, Yevgeny Bar Lev

Published in

Physical review letters. Volume 137. Issue 5. Pages 056603. Jul 31, 2026.

Abstract

We study the full distribution of the zero-temperature Hall conductivity in a lattice model of the integer quantum Hall effect across disorder realizations. Near the plateau transition, the distributions develop heavy power-law tails with exponent α≈2.2-2.5, implying a finite mean but divergent variance. The tail persists across system sizes, correlation lengths of the disorder potential, and fillings indicating that Hall conductivity is not self-averaging at criticality. The exponent is qualitatively compatible with predictions from random-matrix models of Berry curvature fluctuations, hinting at a universal statistical structure of the quantum Hall critical regime.

PMID:
42606469
Bibliographic data and abstract were imported from PubMed on 17 Aug 2026.

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