Internal mobility edge in doped graphene: Frustration in a renormalized lattice

We show that a localization mobility edge can appear around the Fermi energy in graphene by introducing impurities or by producing vacancies in the lattice. The edge appears at the center of the spectrum and not at the band edges, in contrast with the usual picture of localization. Such result is explained by showing that the bipartite nature of the lattice allows one to renormalize the Hamiltonian, and this internal edge appears because of frustration effects in the renormalized lattice. The size in energy of the spectral region with localized states is similar in value to that observed in narrow gap semiconductors.