Abstract
We use the self-consistent mean field approach to study the dispersion relation of graphene on a substrate with hexagonal lattice structure, similar to that of graphene, taking into account on-site Hubbard interactions in the substrate sites. Different Hubbard interactions in the sublattices that constitute the substrate breaks the electron hole symmetry. The interaction between the substrate and the graphene sheet opens two gaps in the dispersion relation of graphene out of the Dirac K point. The position of the gaps depends on the ratio between the first neighbor interaction in graphene and the Hubbard on-site interaction in the substrate lattice.
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