Mode-Shell correspondence, a unifying phase space theory in topological physics -- Part I: Chiral number of zero-modes
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arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2023
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| _version_ | 1866916371409928192 |
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| author | Jezequel, Lucien Delplace, Pierre |
| author_facet | Jezequel, Lucien Delplace, Pierre |
| contents | We propose a theory, that we call the \textit{mode-shell correspondence}, which relates the topological zero-modes localised in phase space to a \textit{shell} invariant defined on the surface forming a shell enclosing these zero-modes. We show that the mode-shell formalism provides a general framework unifying important results of topological physics, such as the bulk-edge correspondence, higher-order topological insulators, but also the Atiyah-Singer and the Callias index theories. In this paper, we discuss the already rich phenomenology of chiral symmetric Hamiltonians where the topological quantity is the chiral number of zero-dimensionial zero-energy modes. We explain how, in a lot of cases, the shell-invariant has a semi-classical limit expressed as a generalised winding number on the shell, which makes it accessible to analytical computations. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2310_05656 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Mode-Shell correspondence, a unifying phase space theory in topological physics -- Part I: Chiral number of zero-modes Jezequel, Lucien Delplace, Pierre Mesoscale and Nanoscale Physics Other Condensed Matter We propose a theory, that we call the \textit{mode-shell correspondence}, which relates the topological zero-modes localised in phase space to a \textit{shell} invariant defined on the surface forming a shell enclosing these zero-modes. We show that the mode-shell formalism provides a general framework unifying important results of topological physics, such as the bulk-edge correspondence, higher-order topological insulators, but also the Atiyah-Singer and the Callias index theories. In this paper, we discuss the already rich phenomenology of chiral symmetric Hamiltonians where the topological quantity is the chiral number of zero-dimensionial zero-energy modes. We explain how, in a lot of cases, the shell-invariant has a semi-classical limit expressed as a generalised winding number on the shell, which makes it accessible to analytical computations. |
| title | Mode-Shell correspondence, a unifying phase space theory in topological physics -- Part I: Chiral number of zero-modes |
| topic | Mesoscale and Nanoscale Physics Other Condensed Matter |
| url | https://arxiv.org/abs/2310.05656 |