Non-Hermitian Hopf insulators
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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_ | 1866916907126358016 |
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| author | Nakamura, Daichi Kawabata, Kohei |
| author_facet | Nakamura, Daichi Kawabata, Kohei |
| contents | Hopf insulators represent a unique class of topological insulators that exist exclusively in two-band systems and are inherently unstable upon the inclusion of additional bands. Meanwhile, recent studies have shown that non-Hermiticity gives rise to distinctive complex-energy gap structures, known as point gaps, and associated topological phases with no analogs in Hermitian systems. However, non-Hermitian counterparts of Hopf insulators have remained largely elusive. Here, we generally classify topological phases of two-band non-Hermitian systems based on the homotopy theory and uncover Hopf-type point-gap topology present only for two bands. Specifically, we reveal such Hopf-type point-gap topology for three-dimensional systems with chiral symmetry (class AIII) and four-dimensional systems with no symmetry (class A). Explicitly constructing prototypical models from the Hermitian Hopf insulator, we further demonstrate that these non-Hermitian topological phases lead to anomalous point-gapless boundary states spectrally detachable from the bulk bands. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2504_15154 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Non-Hermitian Hopf insulators Nakamura, Daichi Kawabata, Kohei Mesoscale and Nanoscale Physics Mathematical Physics Quantum Physics Hopf insulators represent a unique class of topological insulators that exist exclusively in two-band systems and are inherently unstable upon the inclusion of additional bands. Meanwhile, recent studies have shown that non-Hermiticity gives rise to distinctive complex-energy gap structures, known as point gaps, and associated topological phases with no analogs in Hermitian systems. However, non-Hermitian counterparts of Hopf insulators have remained largely elusive. Here, we generally classify topological phases of two-band non-Hermitian systems based on the homotopy theory and uncover Hopf-type point-gap topology present only for two bands. Specifically, we reveal such Hopf-type point-gap topology for three-dimensional systems with chiral symmetry (class AIII) and four-dimensional systems with no symmetry (class A). Explicitly constructing prototypical models from the Hermitian Hopf insulator, we further demonstrate that these non-Hermitian topological phases lead to anomalous point-gapless boundary states spectrally detachable from the bulk bands. |
| title | Non-Hermitian Hopf insulators |
| topic | Mesoscale and Nanoscale Physics Mathematical Physics Quantum Physics |
| url | https://arxiv.org/abs/2504.15154 |