Origin of Robust $\mathbb{Z}_2$ Topological Phases in Stacked Hermitian Systems: Non-Hermitian Level Repulsion
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arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2024
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| _version_ | 1866912142779744256 |
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| author | Jiang, Zhiyu Sato, Masatoshi Obuse, Hideaki |
| author_facet | Jiang, Zhiyu Sato, Masatoshi Obuse, Hideaki |
| contents | Quantum spin Hall insulators, which possess a non-trivial $\mathbb{Z}_2$ topological phase, have attracted great attention for two decades. It is generally believed that when an even number of layers of the quantum spin Hall insulators are stacked, the $\mathbb{Z}_2$ topological phase becomes unstable due to $\mathbb{Z}_2$ nature. While the counterexamples of the instability were observed in several literates, there is no systematic understanding. In this work, we provide a systematic understanding that the robust $\mathbb{Z}_2$ topological phase in a Hermitian system with chiral symmetry against stacking. We clarify that the robustness generally originates from level repulsion in the corresponding non-Hermitian system derived from Hermitization. We demonstrate this by treating a class DIII superconductor in 1D with $\mathbb{Z}_2$ topology and the corresponding non-Hermitian 1D system in class AII$^\dagger$ with $\mathbb{Z}_2$ point-gap topology. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2407_20759 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Origin of Robust $\mathbb{Z}_2$ Topological Phases in Stacked Hermitian Systems: Non-Hermitian Level Repulsion Jiang, Zhiyu Sato, Masatoshi Obuse, Hideaki Mesoscale and Nanoscale Physics Statistical Mechanics Superconductivity Quantum Physics Quantum spin Hall insulators, which possess a non-trivial $\mathbb{Z}_2$ topological phase, have attracted great attention for two decades. It is generally believed that when an even number of layers of the quantum spin Hall insulators are stacked, the $\mathbb{Z}_2$ topological phase becomes unstable due to $\mathbb{Z}_2$ nature. While the counterexamples of the instability were observed in several literates, there is no systematic understanding. In this work, we provide a systematic understanding that the robust $\mathbb{Z}_2$ topological phase in a Hermitian system with chiral symmetry against stacking. We clarify that the robustness generally originates from level repulsion in the corresponding non-Hermitian system derived from Hermitization. We demonstrate this by treating a class DIII superconductor in 1D with $\mathbb{Z}_2$ topology and the corresponding non-Hermitian 1D system in class AII$^\dagger$ with $\mathbb{Z}_2$ point-gap topology. |
| title | Origin of Robust $\mathbb{Z}_2$ Topological Phases in Stacked Hermitian Systems: Non-Hermitian Level Repulsion |
| topic | Mesoscale and Nanoscale Physics Statistical Mechanics Superconductivity Quantum Physics |
| url | https://arxiv.org/abs/2407.20759 |