Localization of generalized Wannier bases implies Chern triviality in non-periodic insulators
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arXiv
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| Formato: | Preprint |
| Publicado: |
2020
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| _version_ | 1866914535642759168 |
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| author | Marcelli, Giovanna Moscolari, Massimo Panati, Gianluca |
| author_facet | Marcelli, Giovanna Moscolari, Massimo Panati, Gianluca |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2012_14407 |
| institution | arXiv |
| publishDate | 2020 |
| record_format | arxiv |
| spellingShingle | Localization of generalized Wannier bases implies Chern triviality in non-periodic insulators Marcelli, Giovanna Moscolari, Massimo Panati, Gianluca Mathematical Physics Mesoscale and Nanoscale Physics 81V70, 81Q70 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. |
| title | Localization of generalized Wannier bases implies Chern triviality in non-periodic insulators |
| topic | Mathematical Physics Mesoscale and Nanoscale Physics 81V70, 81Q70 |
| url | https://arxiv.org/abs/2012.14407 |