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| Main Authors: | , , , |
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| Format: | Preprint |
| Published: |
2026
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2606.00627 |
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| _version_ | 1866910275951656960 |
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| author | Shen, Yekai Chen, Shuhang Liao, Zishun Li, Zhipeng |
| author_facet | Shen, Yekai Chen, Shuhang Liao, Zishun Li, Zhipeng |
| contents | The spectral winding number serves as a bulk topological invariant in non-Hermitian systems, governing the emergence of skin modes and encoding the non-Hermitian bulk-boundary correspondence. However, most existing studies are built on conventional lattice geometries such as linear chains, rings, or planar arrays, leaving the role of real-space topological connectivity as an independent degree of freedom largely unexplored. Here, we construct a Möbius ring system by cutting two parallel Hatano-Nelson (HN) rings and reconnecting them with a half-twist, without altering any local hopping parameter. This topological reconstruction transforms the periodic-boundary spectrum from two disjoint ellipses into a multi-petalled rose curve, and leads to distinct decay lengths for different eigenstates under open boundary conditions. Moreover, the spectral winding number can be driven through discrete winding-number jumps by tuning the coupling strength, with critical values obtained analytically. Our results demonstrate that real-space Möbius connectivity, mediated by the coupling strength, provides an independent and tunable foundation for the systematic control of non-Hermitian topology, with implications for the design of topological devices and sensing schemes. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2606_00627 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Möbius-like Real-Space Topology Reshapes Spectral Winding Topology in Hatano-Nelson Rings Shen, Yekai Chen, Shuhang Liao, Zishun Li, Zhipeng Optics The spectral winding number serves as a bulk topological invariant in non-Hermitian systems, governing the emergence of skin modes and encoding the non-Hermitian bulk-boundary correspondence. However, most existing studies are built on conventional lattice geometries such as linear chains, rings, or planar arrays, leaving the role of real-space topological connectivity as an independent degree of freedom largely unexplored. Here, we construct a Möbius ring system by cutting two parallel Hatano-Nelson (HN) rings and reconnecting them with a half-twist, without altering any local hopping parameter. This topological reconstruction transforms the periodic-boundary spectrum from two disjoint ellipses into a multi-petalled rose curve, and leads to distinct decay lengths for different eigenstates under open boundary conditions. Moreover, the spectral winding number can be driven through discrete winding-number jumps by tuning the coupling strength, with critical values obtained analytically. Our results demonstrate that real-space Möbius connectivity, mediated by the coupling strength, provides an independent and tunable foundation for the systematic control of non-Hermitian topology, with implications for the design of topological devices and sensing schemes. |
| title | Möbius-like Real-Space Topology Reshapes Spectral Winding Topology in Hatano-Nelson Rings |
| topic | Optics |
| url | https://arxiv.org/abs/2606.00627 |