Mobility edge scaling at semiclassical and dissipative Hall transitions

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 $η= 2 x_1 = {1/2}$, 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.