Exact Solutions Disentangle Higher-Order Topology in 2D Non-Hermitian Lattices
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arXiv
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| Main Authors: | , , , , , , |
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| Format: | Preprint |
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2024
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| _version_ | 1866915190379905024 |
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| author | Li, Lingfang Wei, Yating Wu, Gangzhou Ruan, Yang Chen, Shihua Lee, Ching Hua Ni, Zhenhua |
| author_facet | Li, Lingfang Wei, Yating Wu, Gangzhou Ruan, Yang Chen, Shihua Lee, Ching Hua Ni, Zhenhua |
| contents | We report the exact closed-form solutions for higher-order topological states as well as explicit energy-spectrum relationships in two-dimensional (2D) non-Hermitian multi-orbital lattices with generalized boundary conditions. These analytical solutions unequivocally confirm that topological edge states in a 2D non-Hermitian system which feature point-gap topology must undergo the non-Hermitian skin effect along the edge. Under double open boundary conditions, the occurrence of the non-Hermitian skin effect for either topological edge states or bulk states can be accurately predicted by our proposed winding numbers. We unveil that the zero-energy topological corner state only manifests itself on a corner where two nearby gapped edge states intersect, and thus can either disappear completely or strengthen drastically due to the non-Hermitian skin effect of gapped topological edge states. Our analytical results offer direct insight into the non-Bloch band topology in two or higher dimensions and trigger experimental investigations into related phenomena such as quadrupole topological insulators and topological lasing. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_15763 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Exact Solutions Disentangle Higher-Order Topology in 2D Non-Hermitian Lattices Li, Lingfang Wei, Yating Wu, Gangzhou Ruan, Yang Chen, Shihua Lee, Ching Hua Ni, Zhenhua Optics Other Condensed Matter We report the exact closed-form solutions for higher-order topological states as well as explicit energy-spectrum relationships in two-dimensional (2D) non-Hermitian multi-orbital lattices with generalized boundary conditions. These analytical solutions unequivocally confirm that topological edge states in a 2D non-Hermitian system which feature point-gap topology must undergo the non-Hermitian skin effect along the edge. Under double open boundary conditions, the occurrence of the non-Hermitian skin effect for either topological edge states or bulk states can be accurately predicted by our proposed winding numbers. We unveil that the zero-energy topological corner state only manifests itself on a corner where two nearby gapped edge states intersect, and thus can either disappear completely or strengthen drastically due to the non-Hermitian skin effect of gapped topological edge states. Our analytical results offer direct insight into the non-Bloch band topology in two or higher dimensions and trigger experimental investigations into related phenomena such as quadrupole topological insulators and topological lasing. |
| title | Exact Solutions Disentangle Higher-Order Topology in 2D Non-Hermitian Lattices |
| topic | Optics Other Condensed Matter |
| url | https://arxiv.org/abs/2410.15763 |