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

Abstract

The electronic properties of noninteracting 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 $\ensuremath{\rho}(E)$ goes to zero for $E\ensuremath{\rightarrow}0$ 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 $\ensuremath{\rho}(E)$ 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.