Mobility edge scaling at semiclassical and dissipative Hall transitions

TL;DR

This paper derives the universal anomalous diffusion scaling for the semiclassical quantum Hall transition, clarifying discrepancies in previous numerical results and explaining experimental observations of different scaling laws.

Contribution

It provides a theoretical derivation of the anomalous diffusion scaling at the semiclassical Hall transition and explains the crossover to quantum scaling observed in experiments.

Findings

Universal anomalous diffusion scaling derived for semiclassical quantum Hall transition

Explains discrepancy between numerics and expected scaling due to cancellation effects

Describes crossover from semiclassical to quantum scaling with increasing observation time

Abstract

The universal anomalous diffusion scaling is obtained for the semiclassical quantum Hall transition, which has been argued to describe samples with dissipation or correlated impurities. The results explain a discrepancy between existing numerics and the expected scaling $\eta = 2 x_1 = {1/2}$, which is violated because of a cancellation in the scaling function. The crossover with increasing observation time from semiclassical to quantum scaling is shown to explain a recent experiment which finds different scaling laws depending on how the localization length is extracted.