Classification of topological insulators and superconductors with multiple order-two point group symmetries
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arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866911510569156608 |
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| author | Shiozaki, Ken |
| author_facet | Shiozaki, Ken |
| contents | We present a method for computing the classification groups of topological insulators and superconductors in the presence of $\mathbb{Z}_2^{\times n}$ point group symmetries, for arbitrary natural numbers $n$. Each symmetry class is characterized by four possible additional symmetry types for each generator of $\mathbb{Z}_2^{\times n}$, together with bit values encoding whether pairs of generators commute or anticommute. We show that the classification is fully determined by the number of momentum- and real-space variables flipped by each generator, as well as the number of variables simultaneously flipped by any pair of generators. As a concrete illustration, we provide the complete classification table for the case of $\mathbb{Z}_2^{\times 2}$ point group symmetry. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_02168 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Classification of topological insulators and superconductors with multiple order-two point group symmetries Shiozaki, Ken Mesoscale and Nanoscale Physics We present a method for computing the classification groups of topological insulators and superconductors in the presence of $\mathbb{Z}_2^{\times n}$ point group symmetries, for arbitrary natural numbers $n$. Each symmetry class is characterized by four possible additional symmetry types for each generator of $\mathbb{Z}_2^{\times n}$, together with bit values encoding whether pairs of generators commute or anticommute. We show that the classification is fully determined by the number of momentum- and real-space variables flipped by each generator, as well as the number of variables simultaneously flipped by any pair of generators. As a concrete illustration, we provide the complete classification table for the case of $\mathbb{Z}_2^{\times 2}$ point group symmetry. |
| title | Classification of topological insulators and superconductors with multiple order-two point group symmetries |
| topic | Mesoscale and Nanoscale Physics |
| url | https://arxiv.org/abs/2509.02168 |