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.

• Received 29 November 2006

DOI:https://doi.org/10.1103/PhysRevB.75.245401