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.
Original language | English |
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Journal | Communications in Mathematical Physics |
Volume | 397 |
Pages (from-to) | 1163–1190 |
Number of pages | 28 |
ISSN | 0010-3616 |
DOIs | |
Publication status | Published - 2023 |
Bibliographical note
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© 2022, The Author(s), under exclusive licence to Springer-Verlag GmbH Germany, part of Springer Nature.
ID: 328021127