Fredholm Homotopies for Strongly-Disordered 2D Insulators

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  • Alex Bols
  • Jeffrey Schenker
  • Jacob Shapiro

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 languageEnglish
JournalCommunications in Mathematical Physics
Pages (from-to)1163–1190
Number of pages28
Publication statusPublished - 2023

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© 2022, The Author(s), under exclusive licence to Springer-Verlag GmbH Germany, part of Springer Nature.

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