Cross-type spectrum rearrangement in graphene with weakly bound impurity centres: an impurity band with anomalous dispersion.

It is demonstrated that an anomalous dispersion region appears in the energy spectrum of charge carriers in graphene on increasing the concentration of weakly bound impurity centres. The corresponding spectrum rearrangement evolves in the neighbourhood of the impurity resonance energy and is of the cross type. The opening of the anomalous dispersion region in the impure graphene is accompanied by a doubling of the number of Dirac points in its electron spectrum. The stated spectrum rearrangement unfolds in a threshold manner, i.e. it takes place when the impurity concentration exceeds a certain critical value, which is determined by the mutual spatial overlap of individual impurity states.