Density of states of disordered graphene

We calculate the average single-particle density of states in graphene with disorder due to impurity potentials. For unscreened short-ranged impurities, we use the non-self-consistent and self-consistent Born and T-matrix approximations to obtain the self-energy. Among these, only the self-consistent T-matrix approximation gives a nonzero density of states at the Dirac point. The density of states at the Dirac point is nonanalytic in the impurity potential. For screened short-ranged and charged long-range impurity potentials, the density of states near the Dirac point typically increases in the presence of impurities, compared to that of the pure system.