Impurity induced Dirac point smearing in graphene

Abstract

It is shown that in a two-dimensional system with the linear dispersion a resonance is present in the Dirac point vicinity, when the impurity perturbation magnitude exceeds the bandwidth. The corresponding spectrum rearrangement, which follows at a certain critical impurity concentration, results in the square root dependence of the concentration smearing region width on the concentration. If the perturbation magnitude does not exceed the bandwidth, or the critical concentration is not reached, the concentration smearing region width remains exponentially small.