Perturbative Evidence of Non-Universality in the Quantized Hall Conductivity of a Disordered Relativistic 2D Electron Gas

TL;DR

This paper investigates how disorder affects the quantized Hall conductivity in a relativistic 2D electron gas, revealing that disorder can modify the expected quantized values through first-order perturbation analysis.

Contribution

It provides the first perturbative analysis showing non-universality of the quantized Hall conductivity due to disorder in a relativistic 2D electron system.

Findings

Disorder modifies the quantized Hall conductivity values.

First-order perturbation theory captures the impact of a white-noise potential.

Quantization is not strictly universal in the presence of disorder.

Abstract

We study a relativistic two-dimensional electron gas in the presence of a uniform external magnetic field and a random static scalar potential. We compute, in first order perturbation theory, the averages of the charge density and of the transverse conductivity for a white-noise potential, and show that, within this treatment, their quantized values are modified by the disorder.