Topological invariants of band insulators derived from the local-orbital based embedding potential

We demonstrate that topological invariants of band insulators can be derived efficiently from the eigenvalues of the local-orbital (LO) based embedding potential, called also the contact (lead) self-energy. The LO based embedding potential is a bulk quantity. Given the tight-binding Hamiltonian describing the bulk valence and conduction bands, it is constructed straightforwardly from the bulk wave functions satisfying the generalized Bloch condition. When the one-electron energy ɛ is located within a projected bulk band gap at a given planar wave vector k, the embedding potential becomes Hermitian. Its real eigenvalues exhibit distinctly different behavior depending on the topological properties of the valence bands, thus enabling unambiguous identification of bulk topological invariants. We consider the Bernevig-Hughes-Zhang model as an example of a time-reversal invariant topological insulator and tin telluride (SnTe) crystallized in a rock-salt structure as an example of a topological crystalline insulator