The topology of mobility-gapped insulators

Jacob Shapiro

doi:10.1007/s11005-020-01314-9

The topology of mobility-gapped insulators

Jacob Shapiro

Research output: Contribution to journal › Article › peer-review

2 Scopus citations

Abstract

Studying deterministic operators, we define a topology on the space of mobility-gapped insulators such that topological invariants are continuous maps into discrete spaces, we prove that this is indeed the case for the integer quantum Hall effect, and lastly we show why our “insulator” condition makes sense from the point of view of the localization theory using the fractional moments method.

Original language	English (US)
Pages (from-to)	2703-2723
Number of pages	21
Journal	Letters in Mathematical Physics
Volume	110
Issue number	10
DOIs	https://doi.org/10.1007/s11005-020-01314-9
State	Published - Oct 1 2020
Externally published	Yes

All Science Journal Classification (ASJC) codes

Statistical and Nonlinear Physics
Mathematical Physics

Keywords

Integer quantum Hall effect
Mobility gap
Random Schrödinger operators
Strong disorder
Topological insulators

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10.1007/s11005-020-01314-9

Cite this

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AB - Studying deterministic operators, we define a topology on the space of mobility-gapped insulators such that topological invariants are continuous maps into discrete spaces, we prove that this is indeed the case for the integer quantum Hall effect, and lastly we show why our “insulator” condition makes sense from the point of view of the localization theory using the fractional moments method.

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KW - Random Schrödinger operators

KW - Strong disorder

KW - Topological insulators

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The topology of mobility-gapped insulators

Abstract

All Science Journal Classification (ASJC) codes

Keywords

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