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

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.

arXiv comment37 pages, no figures. The text in this version, which corresponds to the paper published in Annales Henri Poincaré, is the updated version of the preprint in v1 entitled "Localization implies Chern triviality in non-periodic insulators". Comparison with v1: title changed, presentation and main result improved, typos fixed, appendix added

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