Bulk-boundary correspondence of topological insulators from their respective Green’s functions
By A. Essin, V. Gurarie. 2011
206 citations recorded by the source corpus.
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.
Subfields: Atomic and Molecular Physics, and Optics, Condensed Matter Physics
View Paper: https://www.semanticscholar.org/paper/b166a3ab5672d0b74eab89c6d390956c68db964b
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In Atomic and Molecular Physics, and Optics
In Condensed Matter Physics
Citations in the corpus
- Colloquium : Topological band theory (2016, background): “While the existence of gapless surface states on the interface of a TI with vacuum or another nontopological material is guaranteed by bulk-boundary correspondence considerations (Hasan and Kane 2010; Essin and Gurarie 2011), an actual computation must be carried out to ascertain the precise nature ”
- K-Theory and Pseudospectra for Topological Insulators (2015, background): “Unlike in [12] and [20], for example, we do not have a separate Hamiltonian for the edge states.”