Bulk-edge correspondence for two-dimensional topological insulators

Abstract

Topological insulators can be characterized alternatively in terms of bulk or edge properties. We prove the equivalence between the two descriptions for two-dimensional solids in the single-particle picture. We give a new formulation of the ${\mathbb{Z}}_2$-invariant, which allows for a bulk index not relying on a (two-dimensional) Brillouin zone. When available though, that index is shown to agree with known formulations. The method also applies to integer quantum Hall systems. We discuss a further variant of the correspondence, based on scattering theory.

45 pages, 9 figures. A gap has been filled in the proof of Theorem 5.7. Typos have been corrected and few references have been added

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