Fredholm Homotopies for Strongly-Disordered 2D Insulators

Alex Bols, Jeffrey Schenker, Jacob Shapiro

Research output: Contribution to journalArticlepeer-review

1 Scopus citations


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 (US)
Pages (from-to)1163-1190
Number of pages28
JournalCommunications In Mathematical Physics
Issue number3
StatePublished - Feb 2023

All Science Journal Classification (ASJC) codes

  • Statistical and Nonlinear Physics
  • Mathematical Physics


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