Publication Date:
2014-12-31
Description:
When a flux quantum is pushed through a gapped two- dimensional tight-binding operator, there is an associated spectral flow through the gap which is shown to be equal to the index of a Fredholm operator encoding the topology of the Fermi projection. This is a natural mathematical formulation of Laughlin’s Gedankenexperiment. It is used to provide yet another proof of the bulk-edge correspondence. Furthermore, when applied to systems with time reversal symmetry, the spectral flow has a characteristic \({\mathbb{Z}_2}\) signature, while for particle–hole symmetric systems it leads to a criterion for the existence of zero energy modes attached to half-flux tubes. Combined with other results, this allows to explain all strong invariants of two-dimensional topological insulators in terms of a single Fredholm operator.
Print ISSN:
1424-0637
Electronic ISSN:
1424-0661
Topics:
Mathematics
,
Physics
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