Localization of generalized Wannier bases implies Chern triviality in non-periodic insulators
arXiv:2012.14407 · doi:10.1007/s00023-022-01232-7
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.
37 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
References in corpus (8)
- Exponential localization of Wannier functions in insulators
- Equality of the bulk and edge Hall conductances in a mobility gap
- The Faraday effect revisited: Thermodynamic limit
- Geometric currents in piezoelectricity
- Tight frames of exponentially decaying Wannier functions
- The Iterated Projected Position Algorithm for Constructing Exponentially Localized Generalized Wannier Functions for Periodic and Non-Periodic Insulators in Two Dimensions and Higher
- Localised module frames and Wannier bases from groupoid Morita equivalences
- Ultra-generalized Wannier bases: Are they relevant to topological transport?
Cited by in corpus (5)
- Compact Wannier Functions in One Dimension
- Topology of ultra-localized insulators and superconductors
- From orbital magnetism to bulk-edge correspondence
- Ultra-generalized Wannier bases: Are they relevant to topological transport?
- On topological obstructions to the existence of non-periodic Wannier bases