Density of states of disordered graphene

TL;DR

This paper investigates how different types of impurity potentials affect the density of states in disordered graphene, revealing that certain approximations predict a non-zero density at the Dirac point and that impurities generally increase the density of states near it.

Contribution

It provides a comparative analysis of various approximation methods for calculating the density of states in disordered graphene, highlighting the significance of the self-consistent T-matrix approximation.

Findings

Self-consistent T-matrix yields non-zero DOS at Dirac point.

DOS at Dirac point is non-analytic in impurity potential.

Impurities increase DOS near the Dirac point.

Abstract

We calculate the average single particle density of states in graphene with disorder due to impurity potentials. For unscreened short-ranged impurities, we use the non-self-consistent and self-consistent Born and $T$-matrix approximations to obtain the self-energy. Among these, only the self-consistent $T$-matrix approximation gives a non-zero density of states at the Dirac point. The density of states at the Dirac point is non-analytic in the impurity potential. For screened short-ranged and charged long-range impurity potentials, the density of states near the Dirac point typically increases in the presence of impurities, compared to that of the pure system.