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arXiv · 2012.14407

Localization of generalized Wannier bases implies Chern triviality in non-periodic insulators

Giovanna Marcelli·Massimo Moscolari·Gianluca Panati
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Abstract

We investigate the relation between the localization of generalized Wannier bases and the topological properties of two-dimensional gapped quantum systems of independent electrons in a disordered background, including magnetic fields, as in the case of Chern insulators and quantum Hall systems. We prove that the existence of a well-localized generalized Wannier basis for the Fermi projection implies the vanishing of the Chern character, which is proportional to the Hall conductivity in the linear response regime. Moreover, we state a localization dichotomy conjecture for general non-periodic gapped quantum systems.

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Giovanna Marcelli, Massimo Moscolari, Gianluca Panati. 2020-12-28. Localization of generalized Wannier bases implies Chern triviality in non-periodic insulators. https://doi.org/10.1007/s00023-022-01232-7

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