Diagrammatic Approach for the High-Temperature Regime of Quantum Hall Transitions

TL;DR

This paper introduces a diagrammatic formalism to analyze high-temperature quantum Hall transitions, revealing a universal scaling exponent for conductance and providing a microscopic expression for experimental analysis.

Contribution

The authors develop a novel diagrammatic approach to study quantum Hall transitions at high temperatures, connecting disorder, dissipation, and classical percolation theory.

Findings

Longitudinal conductance scales with an exponent 0.767

Derived a microscopic expression for temperature-dependent conductance peak

Confirmed the exponent aligns with classical percolation predictions

Abstract

We use a general diagrammatic formalism based on a local conductivity approach to compute electronic transport in continuous media with long-range disorder, in the absence of quantum interference effects. The method allows us then to investigate the interplay of dissipative processes and random drifting of electronic trajectories in the high-temperature regime of quantum Hall transitions. We obtain that the longitudinal conductance \sigma_{xx} scales with an exponent {\kappa}=0.767\pm0.002 in agreement with the value {\kappa}=10/13 conjectured from analogies to classical percolation. We also derive a microscopic expression for the temperature-dependent peak value of \sigma_{xx}, useful to extract {\kappa} from experiments.