Is the Peak Value of $\sigma_{xx}$ at the Quantum Hall Transition Universal?

TL;DR

This paper investigates whether the peak longitudinal conductivity at the quantum Hall transition is universal, proposing a 2D Dirac fermion model with random mass, and finds that conductivity varies with disorder strength, challenging universality.

Contribution

It introduces a 2D Dirac fermion model with random mass to study the quantum Hall transition and demonstrates that the peak conductivity is non-universal, depending on disorder variance.

Findings

Conductivity is reduced by a factor depending on disorder variance g.

Results suggest non-universality of peak conductivity at quantum Hall transition.

Theoretical evidence aligns with experimental observations of non-universality.

Abstract

The question of the universality of the longitudinal peak conductivity at the integer quantum Hall transition is considered. For this purpose, a system of 2D Dirac fermions with random mass characterised by variance $g$ is proposed as a model which undergoes a quantum Hall transition. Whilst for some specific models the longitudinal peak conductivity $\sigma_{xx}$ was found to be universal (in agreement with the conjecture of Lee et al. as well as with some numerical work), we find that $\sigma_{xx}$ is reduced by a factor $(1+g/2\pi)^{-1}$, at least for small $g$. This provides some theoretical evidence for the non-universality of $\sigma_{xx}$, as observed in a number of experiments.