Topological properties of the bond-modulated honeycomb lattice

We study the combined effects of lattice deformation, e−e interaction, and spin-orbit coupling in a two-dimensional (2D) honeycomb lattice. We adopt different kinds of hopping modulation—generalized dimerization and a Kekulé distortion—and calculate topological invariants for the noninteracting system and for the interacting system. We identify the parameter range (Hubbard U, hopping modulation, spin-orbit coupling) where the 2D system behaves as a trivial insulator or quantum spin Hall insulator.