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| Format: | Preprint |
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2025
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| Online-Zugang: | https://arxiv.org/abs/2512.18789 |
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| _version_ | 1866912780580290560 |
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| author | Park, Kyu-Won Kim, KyeongRo Jeong, Kabgyun |
| author_facet | Park, Kyu-Won Kim, KyeongRo Jeong, Kabgyun |
| contents | Chirality is more than a geometric curiosity; it governs measurable asymmetries across nature, from enantiomer-selective drugs and left-handed fermions in particle physics to handed charge transport in Weyl semimetals. We extend this universal concept to non-Hermitian systems by defining topological chirality, an invariant that emerges whenever an exceptional-points (EP) pair is present. Built from the non-commutative fundamental group and its braid representation, topological chirality acts as a singularity selector: clockwise EP loops occupy a homotopy class that avoids EPs, whereas counter-clockwise mirrors are equivalent only if they cross the EPs themselves. We confirm this binary rule in an optical microcavity and a non-Hermitian topological band. The same two-sheeted topology governs EP pairs in spin systems, photonic crystals and hybrid light-matter structures, where EP encirclements have already been demonstrated, so the framework transfers without alteration and confirms its experimental viability. Our findings lay the cornerstone for interpreting loop-sensitive observables such as spectral vorticity, the complex Berry phase and the non-Abelian holonomy. Finally, a gluing-of-planes construction extends the invariant to an n-sheeted surface hosting 2m EPs, unifying higher-order EP pairs. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_18789 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Singularity Selector: Topological Chirality via Non-Abelian Loops around Exceptional Points Park, Kyu-Won Kim, KyeongRo Jeong, Kabgyun Quantum Physics Chirality is more than a geometric curiosity; it governs measurable asymmetries across nature, from enantiomer-selective drugs and left-handed fermions in particle physics to handed charge transport in Weyl semimetals. We extend this universal concept to non-Hermitian systems by defining topological chirality, an invariant that emerges whenever an exceptional-points (EP) pair is present. Built from the non-commutative fundamental group and its braid representation, topological chirality acts as a singularity selector: clockwise EP loops occupy a homotopy class that avoids EPs, whereas counter-clockwise mirrors are equivalent only if they cross the EPs themselves. We confirm this binary rule in an optical microcavity and a non-Hermitian topological band. The same two-sheeted topology governs EP pairs in spin systems, photonic crystals and hybrid light-matter structures, where EP encirclements have already been demonstrated, so the framework transfers without alteration and confirms its experimental viability. Our findings lay the cornerstone for interpreting loop-sensitive observables such as spectral vorticity, the complex Berry phase and the non-Abelian holonomy. Finally, a gluing-of-planes construction extends the invariant to an n-sheeted surface hosting 2m EPs, unifying higher-order EP pairs. |
| title | Singularity Selector: Topological Chirality via Non-Abelian Loops around Exceptional Points |
| topic | Quantum Physics |
| url | https://arxiv.org/abs/2512.18789 |