Using cluster perturbation theory we calculate Greenʼs functions, quasi-particle energies and topological invariants for interacting electrons on a 2D honeycomb lattice, with intrinsic spin-orbit coupling and on-site e-e interaction. This allows us to define the parameter range (Hubbard U versus spinorbit coupling) where the 2D system behaves as a trivial insulator or quantum spin Hall insulator. This behavior is confirmed by the existence of gapless quasi-particle states in honeycomb ribbons. We have discussed the importance of the cluster symmetry and the effects of the lack of full translation symmetry typical of CPT and of most quantum cluster approaches. Comments on the limits of applicability of the method are also provided.
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
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