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 -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.
Bulk-edge correspondence for two-dimensional topological insulators / Graf, G M; Porta, M. - In: COMMUNICATIONS IN MATHEMATICAL PHYSICS. - ISSN 0010-3616. - 324:3(2013), pp. 851-895. [10.1007/s00220-013-1819-6]
Bulk-edge correspondence for two-dimensional topological insulators
Porta M
2013-01-01
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 -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.File | Dimensione | Formato | |
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