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Dirac point metamorphosis from third-neighbor couplings in graphene and related materials

Dirac point metamorphosis from third-neighbor couplings in graphene and related materials

We study the band structure and the density of states of graphene in the presence of a next-to-nearest-neighbor coupling (N2) and a third-nearest-neighbor coupling (N3). We show that for values of N3 larger or equal to 1/3 of the value of the nearest-neighbor hopping (NN), extra Dirac points appear in …