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Using density-functional theory, we calculate the electronic bandstructure ofsingle-layer graphene on top of hexagonal In_2Te_2 monolayers. The geometricconfiguration with In and Te atoms at centers of carbon hexagons leads to aKekule' 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 ischaracterized instead by gapless spectrum with the original Dirac cones ofgraphene reshaped, depending on the graphene-indium chalcogenide distance,either in the form of an undoubled pseudo-spin one Dirac cone or in a quadraticband crossing point at the Fermi level. These electronic phases harbor chargefractionalization and topological Mott insulating states of matter.

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