Abstract
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.
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Communicated by Claude Alain Pillet.
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De Nittis, G., Schulz-Baldes, H. Spectral Flows Associated to Flux Tubes. Ann. Henri Poincaré 17, 1–35 (2016). https://doi.org/10.1007/s00023-014-0394-5
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DOI: https://doi.org/10.1007/s00023-014-0394-5