Fredholm Homotopies for Strongly-Disordered 2D Insulators

Abstract

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 (2005) about the bulk-edge correspondence for strongly-disordered integer quantum Hall systems. We furthermore provide a proof of the stability of the ${\mathbb{Z}}_2$ index in the mobility gap regime. These two-dimensional results serve as a model for the study of higher dimensional ${\mathbb{Z}}_2$ indices.

arXiv comment21 pages, 2 figure

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Cited by in corpus (5)

• On the Bott index of unitary matrices on a finite torus
• Bulk-interface correspondences for one dimensional topological materials with inversion symmetry
• Absolutely continuous edge spectrum of topological insulators with an odd time-reversal symmetry
• From orbital magnetism to bulk-edge correspondence
• Boundary conditions and violations of bulk-edge correspondence in a hydrodynamic model