Fredholm Homotopies for Strongly-Disordered 2D Insulators
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We study topological indices of Fermionic time-reversal invariant topological insulators in two dimensions, in the regime of strong Anderson localization. We devise a method to interpolate between certain Fredholm operators arising in the context of these systems. We use this technique to prove the bulk-edge correspondence for mobility-gapped 2D topological insulators possessing a (Fermionic) time-reversal symmetry (class AII) and provide an alternative route to a theorem by Elgart-Graf-Schenker (Commun Math Phys 259(1):185–221, 2005) about the bulk-edge correspondence for strongly-disordered integer quantum Hall systems. We furthermore provide a proof of the stability of the Z2 index in the mobility gap regime. These two-dimensional results serve as a model for the study of higher dimensional Z2 indices.
Originalsprog | Engelsk |
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Tidsskrift | Communications in Mathematical Physics |
Vol/bind | 397 |
Sider (fra-til) | 1163–1190 |
Antal sider | 28 |
ISSN | 0010-3616 |
DOI | |
Status | Udgivet - 2023 |
Bibliografisk note
Funding Information:
We wish to thank Gian Michele Graf and Martin Zirnbauer for useful discussions. Work on this project was supported in parts by the following grants: A. Bols was supported by the Villium Fonden through the QMATH Centre of Excellence, grant no. 10059. J. Schenker was supported by the U.S. National Science Foundation under Grant No. (1900015). J. Shapiro was supported by the Swiss National Science Foundation (grant number P2EZP2_184228), and the Princeton-Geneva Univ. collaborative travel funds.
Publisher Copyright:
© 2022, The Author(s), under exclusive licence to Springer-Verlag GmbH Germany, part of Springer Nature.
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