Local spectrum rearrangement in impure graphene

The evolution of the averaged local density of states at the impurity site with increasing the impurity concentration is studied by the cluster expansion method for the self-energy. It is demonstrated that the general shape of the local density of states and the decrease rate of the resonance peak height undergo a qualitative change at a certain critical impurity concentration. As a result, the distinctive features in the single-impurity local spectrum are completely smeared out when this critical concentration is exceeded. Within the Lifshitz impurity model, this local spectrum rearrangement is described in detail for the two-dimensional system with the Dirac dispersion of electrons, which is characteristic of graphene. The correspondent critical impurity concentration is related to the spatial overlap of individual impurity states.