Localization properties of Chern insulators
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40598_2019_98_ReferencePDF.pdf
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251.82 KB
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9a3c56a2bab55e4fe2a72bfa8ed8aa09
Author(s)
Bezrukavnikov, Roman
Kapustin, Anton
Date Issued
March 2019
Publisher
Springer International Publishing
Version
Author's final manuscript
Abstract
We study the localization properties of the equal-time electron Green’s function in a Chern insulator in an arbitrary dimension and with an arbitrary number of bands. We prove that the Green’s function cannot decay super-exponentially if the Hamiltonian is finite-range and the quantum Hall response is nonzero. For a general band Hamiltonian (possibly infinite-range), we prove that the Green’s function cannot be finite-range if the quantum Hall response is nonzero. The proofs use methods of algebraic geometry.
MIT Department
Massachusetts Institute of Technology. Department of Mathematics
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Creative Commons Attribution-Noncommercial-Share Alike
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DOI of Published Version
https://doi.org/10.1007/s40598-019-00098-8
