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

Using density-functional theory, we calculate the electronic band structure of single-layer graphene on top of hexagonal ${\mathrm{In}}_2{\mathrm{Te}}_2$ monolayers. The geometric configuration with In and Te atoms at the centers of the carbon hexagons leads to a Kekulé texture with an ensuing band gap 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 a gapless spectrum with the original Dirac cones of graphene reshaped, depending on the graphene-indium chalcogenide distance, either in the form of an undoubled pseudospin-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.

Figure 1

(a) Top view of the two geometrical configurations (A) and (B) of graphene and ${\mathrm{In}}_2{\mathrm{Te}}_2$ layers. (b) Binding energy $\Delta E$ for the two (A) and (B) configurations as a function of the distance $d$ between the graphene sheet and the ${\mathrm{In}}_2{\mathrm{Te}}_2$ monolayer.

Figure 2

(a) Projected density of states with C, In, and Te character. (b) Band structure of the graphene-${\mathrm{In}}_2{\mathrm{Te}}_2$ bilayer for configuration (A) at the equilibrium distance. (c) Band structure of isolated graphene and ${\mathrm{In}}_2{\mathrm{Te}}_2$ single layers.

Figure 3

(a) Values of the band gap as a function of the distance $d$ between graphene and ${\mathrm{In}}_2{\mathrm{Te}}_2$ layers for unrelaxed (S) and relaxed (R) C atomic coordinates. (b) Values of the three inequivalent C-C $\left(d_1,d_2,d_3\right)$ bonds as a function of the distance $d$. (c) Schematic view of the three inequivalent C-C $\left(d_1,d_2,d_3\right)$ bonds for configuration (A). All the data are obtained within LDA.

Figure 4

Band structure of a graphene-${\mathrm{In}}_2{\mathrm{Te}}_2$ bilayer in configuration (B) along high-symmetry directions at some selected layer distances.