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arXiv · 1808.07602

Localization properties of Chern insulators

Roman Bezrukavnikov·Anton Kapustin
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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.

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Roman Bezrukavnikov, Anton Kapustin. 2018-08-23. Localization properties of Chern insulators. https://arxiv.org/abs/1808.07602

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