Density of states of disordered systems with a finite correlation length

TL;DR

This paper introduces a semiclassical approach to accurately compute the density of states in disordered systems with large correlation lengths, applicable beyond perturbative regimes and for non-smooth potentials.

Contribution

It presents a new semiclassical formulation for the DOS that remains accurate for large correlation lengths and non-perturbative, non-smooth disorder potentials.

Findings

Accurate DOS calculation for large correlation length disorder

Convolution expression for DOS involving disorder distribution

Application to Landau level broadening and specific heat

Abstract

We consider a semiclassical formulation for the density of states (DOS) of disordered systems in any dimension. We show that this formulation becomes very accurate when the correlation length of the disorder potential is large. The disorder potential does not need to be smooth and is not limited to the perturbative regime, where the disorder is small. The DOS is expressed in terms of a convolution of the disorder distribution function and the non-disordered DOS. We apply this formalism to evaluate the broadening of Landau levels and to calculate the specific heat in disordered systems.