Impurity induced Dirac point smearing in graphene

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