Effect of weak impurities on electronic properties of graphene: functional renormalization-group analysis

We consider an effect of weak impurities on electronic properties of graphene within the functional renormalization-group approach. The energy dependences of the electronic self-energy and density of states near the neutrality point are discussed. Depending on the symmetry of the impurities, the electronic damping $\Gamma$ and density of states $\rho$ can deviate substantially from those given by the self-consistent Born approximation. We investigate the crossover from the results of the self-consistent Born approximation, which are valid far from the neutrality point to the strong-coupling (diffusive) regime near the neutrality point. For impurities, which are diagonal in both, valley and sublattice indices, we obtain finite density of states at the Fermi level with the values, which are much bigger than the results of the self-consistent Born approximation.