Atiyah-Hirzebruch spectral sequence for topological insulators and superconductors: $E_2$ pages for 1651 magnetic space groups
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arXiv
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| Format: | Preprint |
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2023
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| _version_ | 1866914614945513472 |
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| author | Shiozaki, Ken Ono, Seishiro |
| author_facet | Shiozaki, Ken Ono, Seishiro |
| contents | We compute the $E_2$ pages of the momentum-space and real-space Atiyah-Hirzebruch spectral sequence (AHSS) for topological crystalline insulators and superconductors up to three spatial dimensions, considering the cell decomposition in which if a group action fixes a cell setwise then its group action fixes the same cell pointwise. We provide a detailed description of the implementation for computing the $E_2$ pages of AHSS. Under a physically reasonable assumption, we enumerate all possible $K$-groups that are compatible with the $E_2$ pages for both momentum and real-space AHSS. As a result, we determine the $K$-groups for approximately 59\% of symmetry settings in three spatial dimensions. All the results can be found at this http \href{https://www2.yukawa.kyoto-u.ac.jp/~ken.shiozaki/ahss/e2.html}{URL}. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2304_01827 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Atiyah-Hirzebruch spectral sequence for topological insulators and superconductors: $E_2$ pages for 1651 magnetic space groups Shiozaki, Ken Ono, Seishiro Mesoscale and Nanoscale Physics Superconductivity We compute the $E_2$ pages of the momentum-space and real-space Atiyah-Hirzebruch spectral sequence (AHSS) for topological crystalline insulators and superconductors up to three spatial dimensions, considering the cell decomposition in which if a group action fixes a cell setwise then its group action fixes the same cell pointwise. We provide a detailed description of the implementation for computing the $E_2$ pages of AHSS. Under a physically reasonable assumption, we enumerate all possible $K$-groups that are compatible with the $E_2$ pages for both momentum and real-space AHSS. As a result, we determine the $K$-groups for approximately 59\% of symmetry settings in three spatial dimensions. All the results can be found at this http \href{https://www2.yukawa.kyoto-u.ac.jp/~ken.shiozaki/ahss/e2.html}{URL}. |
| title | Atiyah-Hirzebruch spectral sequence for topological insulators and superconductors: $E_2$ pages for 1651 magnetic space groups |
| topic | Mesoscale and Nanoscale Physics Superconductivity |
| url | https://arxiv.org/abs/2304.01827 |