Braid-protected topological band structures with unpaired exceptional points
We demonstrate the existence of topologically stable unpaired exceptional points (EPs), and construct simple non-Hermitian (NH) tight-binding models exemplifying such remarkable nodal phases. While fermion doubling, i.e., the necessity of compensating the topological charge of a stable nodal point b...
| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
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American Physical Society
2023-10-01
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| Series: | Physical Review Research |
| Online Access: | http://doi.org/10.1103/PhysRevResearch.5.L042010 |
| _version_ | 1827285137260281856 |
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| author | J. Lukas K. König Kang Yang Jan Carl Budich Emil J. Bergholtz |
| author_facet | J. Lukas K. König Kang Yang Jan Carl Budich Emil J. Bergholtz |
| author_sort | J. Lukas K. König |
| collection | DOAJ |
| description | We demonstrate the existence of topologically stable unpaired exceptional points (EPs), and construct simple non-Hermitian (NH) tight-binding models exemplifying such remarkable nodal phases. While fermion doubling, i.e., the necessity of compensating the topological charge of a stable nodal point by an antidote, rules out a direct counterpart of our findings in the realm of Hermitian semimetals, here we derive how nonommuting braids of complex energy levels may stabilize unpaired EPs. Drawing on this insight, we reveal the occurrence of a single, unpaired EP, manifested as a non-Abelian monopole in the Brillouin zone of a minimal three-band model. This third-order degeneracy represents a sweet spot within a larger topological phase that cannot be fully gapped by any local perturbation. Instead, it may only split into simpler (second-order) degeneracies that can only gap out by pairwise annihilation after having moved around inequivalent large circles of the Brillouin zone. Our results imply the incompleteness of a topological classification based on winding numbers, due to non-Abelian representations of the braid group intertwining three or more complex energy levels, and provide insights into the topological robustness of non-Hermitian systems and their non-Abelian phase transitions. |
| first_indexed | 2024-04-24T10:10:02Z |
| format | Article |
| id | doaj.art-ca1f2ce1a7e84dd4b990ae582b38398c |
| institution | Directory Open Access Journal |
| issn | 2643-1564 |
| language | English |
| last_indexed | 2024-04-24T10:10:02Z |
| publishDate | 2023-10-01 |
| publisher | American Physical Society |
| record_format | Article |
| series | Physical Review Research |
| spelling | doaj.art-ca1f2ce1a7e84dd4b990ae582b38398c2024-04-12T17:34:58ZengAmerican Physical SocietyPhysical Review Research2643-15642023-10-0154L04201010.1103/PhysRevResearch.5.L042010Braid-protected topological band structures with unpaired exceptional pointsJ. Lukas K. KönigKang YangJan Carl BudichEmil J. BergholtzWe demonstrate the existence of topologically stable unpaired exceptional points (EPs), and construct simple non-Hermitian (NH) tight-binding models exemplifying such remarkable nodal phases. While fermion doubling, i.e., the necessity of compensating the topological charge of a stable nodal point by an antidote, rules out a direct counterpart of our findings in the realm of Hermitian semimetals, here we derive how nonommuting braids of complex energy levels may stabilize unpaired EPs. Drawing on this insight, we reveal the occurrence of a single, unpaired EP, manifested as a non-Abelian monopole in the Brillouin zone of a minimal three-band model. This third-order degeneracy represents a sweet spot within a larger topological phase that cannot be fully gapped by any local perturbation. Instead, it may only split into simpler (second-order) degeneracies that can only gap out by pairwise annihilation after having moved around inequivalent large circles of the Brillouin zone. Our results imply the incompleteness of a topological classification based on winding numbers, due to non-Abelian representations of the braid group intertwining three or more complex energy levels, and provide insights into the topological robustness of non-Hermitian systems and their non-Abelian phase transitions.http://doi.org/10.1103/PhysRevResearch.5.L042010 |
| spellingShingle | J. Lukas K. König Kang Yang Jan Carl Budich Emil J. Bergholtz Braid-protected topological band structures with unpaired exceptional points Physical Review Research |
| title | Braid-protected topological band structures with unpaired exceptional points |
| title_full | Braid-protected topological band structures with unpaired exceptional points |
| title_fullStr | Braid-protected topological band structures with unpaired exceptional points |
| title_full_unstemmed | Braid-protected topological band structures with unpaired exceptional points |
| title_short | Braid-protected topological band structures with unpaired exceptional points |
| title_sort | braid protected topological band structures with unpaired exceptional points |
| url | http://doi.org/10.1103/PhysRevResearch.5.L042010 |
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