de Nittis G, Schulz-Baldes H (2016)
Publication Type: Journal article, Original article
Publication year: 2016
Publisher: Institute Henri Poincaré
City/Town: to appear in
Book Volume: 17
Pages Range: 1-35
Journal Issue: 1
URI: http://link.springer.com/article/10.1007/s00023-014-0394-5
DOI: 10.1007/s00023-014-0394-5
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.
APA:
de Nittis, G., & Schulz-Baldes, H. (2016). Spectral flows associated to flux tubes. Annales Henri Poincaré, 17(1), 1-35. https://dx.doi.org/10.1007/s00023-014-0394-5
MLA:
de Nittis, Giuseppe, and Hermann Schulz-Baldes. "Spectral flows associated to flux tubes." Annales Henri Poincaré 17.1 (2016): 1-35.
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