Impurity effects in a two-dimensional system with the Dirac spectrum

It is demonstrated that in a two-band two-dimensional system resonance state is manifested close to the energy of the Dirac point in the electron spectrum for a sufficiently large impurity perturbation. With increasing impurity concentration, the electron spectrum undergoes a rearrangement, which is characterized by the opening of a broad quasigap in the vicinity of the nodal point. If the critical concentration for the spectrum rearrangement is not reached, the domain of localized states remains exponentially small compared to the bandwidth.