Atiyah-Hirzebruch spectral sequence for topological insulators and superconductors: E2 pages for 1651 magnetic space groups
Ken Shiozaki, Seishiro Ono
DOI 10.1103/bvfl-ff5t · Physical Review B
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Abstract
We compute the E2 pages of the momentum-space and real-space Atiyah-Hirzebruch spectral sequence (AHSS) for topological crystalline insulators and superconductors up to three spatial dimensions, using cell decompositions such that any group element that fixes a cell setwise also fixes it pointwise. We provide a detailed description of the implementation for computing the E2 pages of AHSS. Under a physically reasonable assumption, we enumerate all possible K-groups that are compatible with the E2 pages for both momentum and real-space AHSS. As a result, we determined the K-groups for approximately 59% of symmetry settings in three spatial dimensions.
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