Electronic states in graphene on hexagonal substrates

Using a symmetry-based approach, I discuss generic miniband structures for electrons in graphene placed on insulating hexagonal substrates. I focus on two types of crystals: I) with lattice constant close to that of grapheme and II) with a unit cell approximately three times larger than that of graphene. For the first group, I identify conditions at which the first moire miniband is separated from the rest of the spectrum by either one or a group of three isolated mini Dirac points and is not obscured by dispersion surfaces coming from other minibands. I also investigate the influence of magnetic field on the miniband structure and compare the theoretical predictions to magnetotransport measurements performed on graphene/hBN heterostructures, including the evidence for Hofstadter's butterfly. For the second group of substrates, I show that the miniband formation occurs due to periodically modulated intervalley scattering. In contrast to the perfectly commensurate Kekule distortion of graphene, such superlattice perturbation leaves the zero-energy Dirac cones intact, but is able to open a band gap at the edge of the first moire subbands, asymmetrically in the conduction and valence bands. I suggest materials which may fall within the second group of
substrates.