Local spectrum rearrangement in impure graphene

Received 29 November 2006; revised manuscript received 8 May 2007; published 4 June 2007The evolution of the averaged local density of states at the impurity site with increasing the impurityconcentration is studied by the cluster expansion method for the self-energy. It is demonstrated that the generalshape of the local density of states and the decrease rate of the resonance peak height undergo a qualitativechange at a certain critical impurity concentration. As a result, the distinctive features in the single-impuritylocal spectrum are completely smeared out when this critical concentration is exceeded. Within the Lifshitzimpurity model, this local spectrum rearrangement is described in detail for the two-dimensional system withthe Dirac dispersion of electrons, which is characteristic of graphene. The correspondent critical impurityconcentration is related to the spatial overlap of individual impurity states.DOI: 10.1103/PhysRevB.75.245401 PACS number s : 71.23. k, 71.55. i, 81.05.Uw