Transport via classical percolation at quantum Hall plateau transitions

TL;DR

This paper models the peak longitudinal conductivity at quantum Hall transitions using a classical percolation framework, incorporating disorder, drift motion, and inelastic scattering, and derives a scaling function to extract universal critical exponents.

Contribution

It introduces a diagrammatic solution for classical percolation effects in quantum Hall transport, linking theoretical predictions with experimental critical exponents.

Findings

Derived a scaling function for peak conductivity at high temperatures.

Identified the role of classical percolation in quantum Hall plateau transitions.

Provided a method to extract universal critical exponents from experimental data.

Abstract

We consider transport properties of disordered two-dimensional electron gases under high perpendicular magnetic field, focusing in particular on the peak longitudinal conductivity $\sigma_{xx}^\mathrm{peak}$ at the quantum Hall plateau transition. We use a local conductivity model, valid at temperatures high enough such that quantum tunneling is suppressed, taking into account the random drift motion of the electrons in the disordered potential landscape and inelastic processes provided by electron-phonon scattering. A diagrammatic solution of this problem is proposed, which leads to a rich interplay of conduction mechanisms, where classical percolation effects play a prominent role. The scaling function for $\sigma_{xx}^\mathrm{peak}$ is derived in the high temperature limit, which can be used to extract universal critical exponents of classical percolation from experimental data.