Response to polarization and weak topology in Chern insulators
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arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2023
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| _version_ | 1866916663255891968 |
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| author | Vaidya, Sachin Rechtsman, Mikael C. Benalcazar, Wladimir A. |
| author_facet | Vaidya, Sachin Rechtsman, Mikael C. Benalcazar, Wladimir A. |
| contents | Chern insulators present a topological obstruction to a smooth gauge in their Bloch wave functions that prevents the construction of exponentially-localized Wannier functions - this makes the electric polarization ill-defined. Here, we show that spatial or temporal differences in polarization within Chern insulators are well-defined and physically meaningful because they account for bound charges and adiabatic currents. We further show that the difference in polarization across Chern-insulator regions can be quantized in the presence of crystalline symmetries, leading to "weak" symmetry-protected topological phases. These phases exhibit charge fractional quantization at the edge and corner interfaces and with concomitant topological states. We also generalize our findings to quantum spin-Hall insulators and 3D topological insulators. Our work settles a long-standing question and deems the bulk polarization as the fundamental quantity with a "bulk-boundary correspondence", regardless of whether a Wannier representation is possible. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2304_13118 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Response to polarization and weak topology in Chern insulators Vaidya, Sachin Rechtsman, Mikael C. Benalcazar, Wladimir A. Mesoscale and Nanoscale Physics Optics Chern insulators present a topological obstruction to a smooth gauge in their Bloch wave functions that prevents the construction of exponentially-localized Wannier functions - this makes the electric polarization ill-defined. Here, we show that spatial or temporal differences in polarization within Chern insulators are well-defined and physically meaningful because they account for bound charges and adiabatic currents. We further show that the difference in polarization across Chern-insulator regions can be quantized in the presence of crystalline symmetries, leading to "weak" symmetry-protected topological phases. These phases exhibit charge fractional quantization at the edge and corner interfaces and with concomitant topological states. We also generalize our findings to quantum spin-Hall insulators and 3D topological insulators. Our work settles a long-standing question and deems the bulk polarization as the fundamental quantity with a "bulk-boundary correspondence", regardless of whether a Wannier representation is possible. |
| title | Response to polarization and weak topology in Chern insulators |
| topic | Mesoscale and Nanoscale Physics Optics |
| url | https://arxiv.org/abs/2304.13118 |