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arXiv · 1405.2054

Spectral flows associated to flux tubes

Giuseppe De Nittis·Hermann Schulz-Baldes
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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 $Z_2$ 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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Giuseppe De Nittis, Hermann Schulz-Baldes. 2015-02-27. Spectral flows associated to flux tubes. https://doi.org/10.1007/s00023-014-0394-5

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