Physics – Condensed Matter – Mesoscale and Nanoscale Physics
Scientific paper
2011-04-08
Phys. Rev. B 84, 125132 (2011)
Physics
Condensed Matter
Mesoscale and Nanoscale Physics
6.5 pages + appendices; significantly expanded explanations
Scientific paper
10.1103/PhysRevB.84.125132
Topological insulators are noninteracting, gapped fermionic systems which have gapless boundary excitations. They are characterized by topological invariants, which can be written in many different ways, including in terms of Green's functions. Here we show that the existence of the edge states directly follows from the existence of the topological invariant written in terms of the Green's functions, for all ten classes of topological insulators in all spatial dimensions. We also show that the resulting edge states are characterized by their own topological invariant, whose value is equal to the topological invariant of the bulk insulator. This can be used to test whether a given model Hamiltonian can describe an edge of a topological insulator. Finally, we observe that the results discussed here apply equally well to interacting topological insulators, with certain modifications.
Essin Andrew M.
Gurarie Victor
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