Doped graphene: the interplay between localization and frustration due to the underlying triangular symmetry

An intuitive explanation of the increase in localization observed near the Dirac point in doped graphene is presented. To do this, we renormalize the tight binding Hamiltonians in such a way that the honeycomb lattice maps into a triangular one. Then, we investigate the frustration effects that emerge in this Hamiltonian. In this doped triangular lattice, the eigenstates have a bonding and antibonding contribution near the Dirac point, and thus there is a kind of Lifshitz tail. The increase in frustration is related to an increase in localization, since the number of frustrated bonds decreases with disorder, while the frustration contribution raises.