Two-dimensional electron gas in a uniform magnetic field in the presence of a delta-impurity

TL;DR

This paper provides an exact, gauge-invariant calculation of the density of states and Hall conductivity for a 2D electron gas with a delta impurity in a magnetic field, offering a versatile approach for similar problems.

Contribution

It introduces a gauge-invariant method for calculating electronic properties in a 2D electron gas with delta impurities, adaptable to other delta potential problems.

Findings

Exact calculation of density of states and Hall conductivity

Gauge-invariant treatment of delta impurity effects

Method applicable to other delta potential problems

Abstract

The density of states and the Hall conductivity of a two-dimensional electron gas in a uniform magnetic field and in the presence of a delta impurity are exactly calculated using elementary field theoretic techniques. Although these results are not new, our treatment is explicitly gauge-invariant, and can be easily adapted to other problems involving a delta potential.