Exceptional topology on nonorientable manifolds
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arXiv
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| Main Authors: | , , , , , |
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| Format: | Preprint |
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2025
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| _version_ | 1866914426144161792 |
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| author | König, J. Lukas K. Yang, Kang Fonseca, André Grossi Vaidya, Sachin Soljačić, Marin Bergholtz, Emil J. |
| author_facet | König, J. Lukas K. Yang, Kang Fonseca, André Grossi Vaidya, Sachin Soljačić, Marin Bergholtz, Emil J. |
| contents | We classify gapped phases and characteristic nodal points of non-Hermitian band structures on two-dimensional nonorientable parameter spaces. Such spaces arise in a wide range of physical systems in the presence of nonsymmorphic parameter space symmetries. For gapped phases, we find that nonorientable spaces provide a natural setting for exploring fundamental structural problems in braid group theory, such as torsion and conjugacy. Gapless systems, which host exceptional points (EPs), explicitly violate fermion doubling, even in two-band models. We demonstrate that EPs traversing the nonorientable parameter space exhibit non-Abelian charge inversion. These braided phases and their transitions leave distinct signatures in the form of bulk Fermi arc degeneracies, offering a concrete route toward experimental realization and verification. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2503_04889 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Exceptional topology on nonorientable manifolds König, J. Lukas K. Yang, Kang Fonseca, André Grossi Vaidya, Sachin Soljačić, Marin Bergholtz, Emil J. Mesoscale and Nanoscale Physics Mathematical Physics Optics Quantum Physics We classify gapped phases and characteristic nodal points of non-Hermitian band structures on two-dimensional nonorientable parameter spaces. Such spaces arise in a wide range of physical systems in the presence of nonsymmorphic parameter space symmetries. For gapped phases, we find that nonorientable spaces provide a natural setting for exploring fundamental structural problems in braid group theory, such as torsion and conjugacy. Gapless systems, which host exceptional points (EPs), explicitly violate fermion doubling, even in two-band models. We demonstrate that EPs traversing the nonorientable parameter space exhibit non-Abelian charge inversion. These braided phases and their transitions leave distinct signatures in the form of bulk Fermi arc degeneracies, offering a concrete route toward experimental realization and verification. |
| title | Exceptional topology on nonorientable manifolds |
| topic | Mesoscale and Nanoscale Physics Mathematical Physics Optics Quantum Physics |
| url | https://arxiv.org/abs/2503.04889 |