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Localization of Generalized Wannier Bases Implies Chern Triviality in Non-periodic Insulators
Giovanna Marcelli1, Massimo Moscolari2, Gianluca Panati3
1Mathematics Area, SISSA, Via Bonomea 265, 34136 Trieste, Italy.
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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