Bulk-boundary correspondence of topological insulators from their respective Green’s functions

Topological insulators are noninteracting, gapped fermionic systems which\nhave gapless boundary excitations. They are characterized by topological\ninvariants, which can be written in many different ways, including in terms of\nGreen's functions. Here we show that the existence of the edge states directly\nfollows from the existence of the topological invariant written in terms of the\nGreen's functions, for all ten classes of topological insulators in all spatial\ndimensions. We also show that the resulting edge states are characterized by\ntheir own topological invariant, whose value is equal to the topological\ninvariant of the bulk insulator. This can be used to test whether a given model\nHamiltonian can describe an edge of a topological insulator. Finally, we\nobserve that the results discussed here apply equally well to interacting\ntopological insulators, with certain modifications.\n