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

Abstract

It is demonstrated that in a two--band 2D system the resonance state is manifested close to the energy of the Dirac point in the electron spectrum for the sufficiently large impurity perturbation. With increasing the impurity concentration, the electron spectrum undergoes the rearrangement, which is characterized by the opening of the broad quasi--gap 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.