The weakly disordered 2D electron gas in a magnetic field

TL;DR

This paper investigates the behavior of a relativistic 2D electron gas under magnetic fields and disorder, analyzing charge density and conductivity through perturbation theory, and examining the impact of disorder correlation length.

Contribution

It provides a first-order perturbative analysis of charge density and conductivity in a relativistic 2D electron gas with disorder, highlighting the role of correlation length.

Findings

Charge density and conductivity are computed in the presence of disorder.

The effect of disorder correlation length on physical properties is discussed.

First-order perturbation theory is used to analyze the system.

Abstract

We study a relativistic two-dimensional free electron gas in the presence of a uniform external magnetic field and a random static scalar potential. We compute the expectation values of the charge density and the conductivity tensor, averaged over the random potential in first order perturbation theory. We discuss the effect of a zero vs. finite range correlation length of the random potential.