Fredholm Homotopies for Strongly-Disordered 2D Insulators
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Fredholm Homotopies for Strongly-Disordered 2D Insulators. / Bols, Alex; Schenker, Jeffrey; Shapiro, Jacob.
In: Communications in Mathematical Physics, Vol. 397, 2023, p. 1163–1190.Research output: Contribution to journal › Journal article › Research › peer-review
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TY - JOUR
T1 - Fredholm Homotopies for Strongly-Disordered 2D Insulators
AU - Bols, Alex
AU - Schenker, Jeffrey
AU - Shapiro, Jacob
N1 - Publisher Copyright: © 2022, The Author(s), under exclusive licence to Springer-Verlag GmbH Germany, part of Springer Nature.
PY - 2023
Y1 - 2023
N2 - 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.
AB - 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.
UR - http://www.scopus.com/inward/record.url?scp=85142298772&partnerID=8YFLogxK
U2 - 10.1007/s00220-022-04511-w
DO - 10.1007/s00220-022-04511-w
M3 - Journal article
AN - SCOPUS:85142298772
VL - 397
SP - 1163
EP - 1190
JO - Communications in Mathematical Physics
JF - Communications in Mathematical Physics
SN - 0010-3616
ER -
ID: 328021127