Braids and Higher-order Exceptional Points from the Interplay Between Lossy Defects and Topological Boundary States
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arXiv
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| Hauptverfasser: | , , , |
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| Format: | Preprint |
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2023
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| _version_ | 1866910647083597824 |
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| author | Li, Zi-Jian Cardoso, Gabriel Bergholtz, Emil J. Jiang, Qing-Dong |
| author_facet | Li, Zi-Jian Cardoso, Gabriel Bergholtz, Emil J. Jiang, Qing-Dong |
| contents | We show that the perturbation of the Su-Schrieffer-Heeger chain by a localized lossy defect leads to higher-order exceptional points (HOEP). Depending on the location of the defect, third- and fourth- order exceptional points (EP3 \& EP4) appear in the space of Hamiltonian parameters. On the one hand, they arise due to the non-Abelian braiding properties of exceptional lines (EL) in parameter space. Namely, the HOEPs lie at intersections of mutually non-commuting ELs. On the other hand, we show that such special intersections happen due to the fact that the delocalization of edge states, induced by the non-Hermitian defect, hybridizes them with defect states. These can then coalesce together into an EP3. When the defect lies at the midpoint of the chain, a special symmetry of the full spectrum can lead to an EP4. In this way, our model illustrates the emergence of interesting non-Abelian topological properties in the multiband structure of non-Hermitian perturbations of topological phases. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2312_03054 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Braids and Higher-order Exceptional Points from the Interplay Between Lossy Defects and Topological Boundary States Li, Zi-Jian Cardoso, Gabriel Bergholtz, Emil J. Jiang, Qing-Dong Mesoscale and Nanoscale Physics Mathematical Physics Optics Quantum Physics We show that the perturbation of the Su-Schrieffer-Heeger chain by a localized lossy defect leads to higher-order exceptional points (HOEP). Depending on the location of the defect, third- and fourth- order exceptional points (EP3 \& EP4) appear in the space of Hamiltonian parameters. On the one hand, they arise due to the non-Abelian braiding properties of exceptional lines (EL) in parameter space. Namely, the HOEPs lie at intersections of mutually non-commuting ELs. On the other hand, we show that such special intersections happen due to the fact that the delocalization of edge states, induced by the non-Hermitian defect, hybridizes them with defect states. These can then coalesce together into an EP3. When the defect lies at the midpoint of the chain, a special symmetry of the full spectrum can lead to an EP4. In this way, our model illustrates the emergence of interesting non-Abelian topological properties in the multiband structure of non-Hermitian perturbations of topological phases. |
| title | Braids and Higher-order Exceptional Points from the Interplay Between Lossy Defects and Topological Boundary States |
| topic | Mesoscale and Nanoscale Physics Mathematical Physics Optics Quantum Physics |
| url | https://arxiv.org/abs/2312.03054 |