Narrow depression in the density of states at the Dirac point in disordered graphene

TL;DR

This study numerically investigates how disorder and magnetic fields affect the density of states near the Dirac point in graphene, revealing a steep depression that can be filled by short-range disorder.

Contribution

It provides a detailed numerical analysis of the density of states near the Dirac point under various disorder and magnetic field conditions, extending previous analytical models.

Findings

Density of states approaches zero at the Dirac point with a steep slope.

Short-range disorder fills the depression in the density of states.

The dependence of the density of states on system size and disorder matches analytical predictions.

Abstract

The electronic properties of non-interacting particles moving on a two-dimensional bricklayer lattice are investigated numerically. In particular, the influence of disorder in form of a spatially varying random magnetic flux is studied. In addition, a strong perpendicular constant magnetic field $B$ is considered. The density of states $\rho(E)$ goes to zero for $E\to 0$ as in the ordered system, but with a much steeper slope. This happens for both cases: at the Dirac point for B=0 and at the center of the central Landau band for finite $B$. Close to the Dirac point, the dependence of $\rho(E)$ on the system size, on the disorder strength, and on the constant magnetic flux density is analyzed and fitted to an analytical expression proposed previously in connection with the thermal quantum Hall effect. Additional short-range on-site disorder completely replenishes the indentation in the density of states at the Dirac point.