Bulk-boundary correspondence in point-gap topological phases
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arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
| Veröffentlicht: |
2022
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| _version_ | 1866917625468026880 |
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| author | Nakamura, Daichi Bessho, Takumi Sato, Masatoshi |
| author_facet | Nakamura, Daichi Bessho, Takumi Sato, Masatoshi |
| contents | A striking feature of non-Hermitian systems is the presence of two different types of topology. One generalizes Hermitian topological phases, and the other is intrinsic to non-Hermitian systems, which are called line-gap topology and point-gap topology, respectively. Whereas the bulk-boundary correspondence is a fundamental principle in the former topology, its role in the latter has not been clear yet. This Letter establishes the bulk-boundary correspondence in the point-gap topology in non-Hermitian systems. After revealing the requirement for point-gap topology in the open boundary conditions, we clarify that the bulk point-gap topology in open boundary conditions can be different from that in periodic boundary conditions. On the basis of real space topological invariants and the $K$-theory, we give a complete classification of the open boundary point-gap topology with symmetry and show that the nontrivial open boundary topology results in robust and exotic surface states. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2205_15635 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Bulk-boundary correspondence in point-gap topological phases Nakamura, Daichi Bessho, Takumi Sato, Masatoshi Mesoscale and Nanoscale Physics Mathematical Physics Quantum Physics A striking feature of non-Hermitian systems is the presence of two different types of topology. One generalizes Hermitian topological phases, and the other is intrinsic to non-Hermitian systems, which are called line-gap topology and point-gap topology, respectively. Whereas the bulk-boundary correspondence is a fundamental principle in the former topology, its role in the latter has not been clear yet. This Letter establishes the bulk-boundary correspondence in the point-gap topology in non-Hermitian systems. After revealing the requirement for point-gap topology in the open boundary conditions, we clarify that the bulk point-gap topology in open boundary conditions can be different from that in periodic boundary conditions. On the basis of real space topological invariants and the $K$-theory, we give a complete classification of the open boundary point-gap topology with symmetry and show that the nontrivial open boundary topology results in robust and exotic surface states. |
| title | Bulk-boundary correspondence in point-gap topological phases |
| topic | Mesoscale and Nanoscale Physics Mathematical Physics Quantum Physics |
| url | https://arxiv.org/abs/2205.15635 |