Higher-order Topological Knots and the classification of non-Hermitian lattices under $C_n$ symmetry
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arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866908372617396224 |
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| author | Wang, Yifan Benalcazar, Wladimir A. |
| author_facet | Wang, Yifan Benalcazar, Wladimir A. |
| contents | In two dimensions, Hermitian lattices with non-zero Chern numbers and non-Hermitian lattices with a higher-order skin effect (HOSE) bypass the constraints of the Nielsen-Ninomiya no-go theorem at their one-dimensional boundaries. This allows the realization of topologically-protected one-dimensional edges with nonreciprocal dynamics. However, unlike the edge states of Chern insulators, the nonreciprocal edges of HOSE phases exist only at certain edges of the two-dimensional lattice, not all, leading to corner-localized states. In this paper, we investigate the topological connections between these two systems and uncover novel non-Hermitian topological phases possessing higher-order topological knots (HOTKs). These phases arise from multiband topology protected by crystalline symmetries and host nonreciprocal edge states that circulate the entire boundary of the two-dimensional lattice. We show that phase transitions typically separate HOTK phases from complex Chern insulator phases - non-Hermitian lattices with nonzero Chern numbers protected by imaginary line gaps in the presence of time-reversal symmetry. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2412_05809 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Higher-order Topological Knots and the classification of non-Hermitian lattices under $C_n$ symmetry Wang, Yifan Benalcazar, Wladimir A. Mesoscale and Nanoscale Physics In two dimensions, Hermitian lattices with non-zero Chern numbers and non-Hermitian lattices with a higher-order skin effect (HOSE) bypass the constraints of the Nielsen-Ninomiya no-go theorem at their one-dimensional boundaries. This allows the realization of topologically-protected one-dimensional edges with nonreciprocal dynamics. However, unlike the edge states of Chern insulators, the nonreciprocal edges of HOSE phases exist only at certain edges of the two-dimensional lattice, not all, leading to corner-localized states. In this paper, we investigate the topological connections between these two systems and uncover novel non-Hermitian topological phases possessing higher-order topological knots (HOTKs). These phases arise from multiband topology protected by crystalline symmetries and host nonreciprocal edge states that circulate the entire boundary of the two-dimensional lattice. We show that phase transitions typically separate HOTK phases from complex Chern insulator phases - non-Hermitian lattices with nonzero Chern numbers protected by imaginary line gaps in the presence of time-reversal symmetry. |
| title | Higher-order Topological Knots and the classification of non-Hermitian lattices under $C_n$ symmetry |
| topic | Mesoscale and Nanoscale Physics |
| url | https://arxiv.org/abs/2412.05809 |