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

Harvard

Bols, A, Schenker, J & Shapiro, J 2023, 'Fredholm Homotopies for Strongly-Disordered 2D Insulators', Communications in Mathematical Physics, vol. 397, pp. 1163–1190. https://doi.org/10.1007/s00220-022-04511-w

APA

Bols, A., Schenker, J., & Shapiro, J. (2023). Fredholm Homotopies for Strongly-Disordered 2D Insulators. Communications in Mathematical Physics, 397, 1163–1190. https://doi.org/10.1007/s00220-022-04511-w

Vancouver

Bols A, Schenker J, Shapiro J. Fredholm Homotopies for Strongly-Disordered 2D Insulators. Communications in Mathematical Physics. 2023;397:1163–1190. https://doi.org/10.1007/s00220-022-04511-w

Author

Bols, Alex ; Schenker, Jeffrey ; Shapiro, Jacob. / Fredholm Homotopies for Strongly-Disordered 2D Insulators. In: Communications in Mathematical Physics. 2023 ; Vol. 397. pp. 1163–1190.

Bibtex

@article{cb9b0fa1aae247baa7abad60b11bb1b1,
title = "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 (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.",
author = "Alex Bols and Jeffrey Schenker and Jacob Shapiro",
note = "Publisher Copyright: {\textcopyright} 2022, The Author(s), under exclusive licence to Springer-Verlag GmbH Germany, part of Springer Nature.",
year = "2023",
doi = "10.1007/s00220-022-04511-w",
language = "English",
volume = "397",
pages = "1163–1190",
journal = "Communications in Mathematical Physics",
issn = "0010-3616",
publisher = "Springer",

}

RIS

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