Supplementary Data for arXiv:2311.15814

User Guide

Here, we provide supplementary data to understand results in arXiv:2311:15814

Seishiro Ono* and Ken Shiozaki*, "Towards complete characterization of topological insulators and superconductors: A systematic construction of topological invariants based on Atiyah-Hirzebruch spectral sequence", arXiv:2311.15814.

(*The authors contributed equally)

If you have any questions or comments, please contact seishiro.ono[at]riken.jp

[Last update: December 21, 2023]

Cell Decomposition

Normal conducting phases Superconducting phases

Irreducible representations

Spinful normal conducting phases Spinless normal conducting phases Class D spinful superconducting phases Class D spinless superconducting phases Class C spinful superconducting phases Class C spinless superconducting phases

Matrices for invariants

Spinful normal conducting phases Spinless normal conducting phases Class D spinful superconducting phases Class D spinless superconducting phases Class C spinful superconducting phases Class C spinless superconducting phases

Corresponding between space groups and magnetic space groups

SG to MSG

Numerical Data

Raw data of numerical calculations (available only for Mathematica or Wolfram Engine)