On the effect of weak disorder on the density of states in graphene

TL;DR

This paper investigates how weak disorder affects the density of states in graphene, revealing a transition from linear to non-universal power-law behavior and its implications for conductivity.

Contribution

It introduces a comparison between self-consistent non-crossing approximation and perturbation theory to analyze disorder effects on graphene's density of states.

Findings

Density of states shifts from linear to power-law with disorder

Exponent of density of states depends on disorder strength

Non-linear density of states can still produce conductivity proportional to charge carriers

Abstract

The effect of weak potential and bond disorder on the density of states of graphene is studied. By comparing the self-consistent non-crossing approximation on the honeycomb lattice with perturbation theory on the Dirac fermions, we conclude, that the linear density of states of pure graphene changes to a non-universal power-law, whose exponent depends on the strength of disorder like 1-4g/sqrt{3}t^2\pi, with g the variance of the Gaussian disorder, t the hopping integral. This can result in a significant suppression of the exponent of the density of states in the weak-disorder limit. We argue, that even a non-linear density of states can result in a conductivity being proportional to the number of charge carriers, in accordance with experimental findings.