Topological Properties of Electrons in Honeycomb Lattice with Kekulé Hopping Textures

Abstract: Honeycomb lattice can support electronic states exhibiting Dirac energy dispersion, with graphene as the icon. We propose to derive nontrivial topology by grouping six neighboring sites of honeycomb lattice into hexagons and enhancing the inter-hexagon hopping energies over the intra-hexagon ones. We reveal that this manipulation opens a gap in the energy dispersion and drives the system into a topological state. The nontrivial topology is characterized by the $\mathbb{Z}_2$ index associated with a pseudo time-reversal symmetry emerging from the $C_6$ symmetry of the Kekul\'{e} hopping texture, where the angular momentum of orbitals accommodated on the hexagonal "artificial atoms" behaves as the pseudospin. The size of topological gap is proportional to the hopping-integral difference, which can be larger than typical spin-orbit couplings by orders of magnitude and potentially renders topological electronic transports available at high temperatures.