Kekule textures, pseudospin-one Dirac cones, and quadratic band crossings in a graphene-hexagonal indium chalcogenide bilayer

Using density-functional theory, we calculate the electronic bandstructure of single-layer graphene on top of hexagonal In_2Te_2 monolayers. The geometric configuration with In and Te atoms at centers of carbon hexagons leads to a Kekule' texture with an ensuing bandgap of 20 meV. The alternative structure, nearly degenerate in energy, with the In and Te atoms on top of carbon sites is characterized instead by gapless spectrum with the original Dirac cones of graphene reshaped, depending on the graphene-indium chalcogenide distance, either in the form of an undoubled pseudo-spin one Dirac cone or in a quadratic band crossing point at the Fermi level. These electronic phases harbor charge fractionalization and topological Mott insulating states of matter.