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.

Marcelli, G., Moscolari, M., Panati, G. (2023). Localization of Generalized Wannier Bases Implies Chern Triviality in Non-periodic Insulators. ANNALES HENRI POINCARE', 24(3), 895-930 [10.1007/s00023-022-01232-7].

Localization of Generalized Wannier Bases Implies Chern Triviality in Non-periodic Insulators

Marcelli G.;
2023-01-01

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.
2023
Marcelli, G., Moscolari, M., Panati, G. (2023). Localization of Generalized Wannier Bases Implies Chern Triviality in Non-periodic Insulators. ANNALES HENRI POINCARE', 24(3), 895-930 [10.1007/s00023-022-01232-7].
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11590/472933
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