Magnetic Topological Quantum Chemistry

In [Bradlyn et al., Nature (2017)], we introduced Topological Quantum Chemistry (TQC) - a real-space predictive theory of band topology and degeneracy constructed from graph theory and atomic orbitals in the 230 time-reversal- (T-) symmetric space groups (SGs). TQC subsequently fueled the identification of tens of thousands of topological materials, and the discovery of novel topological insulating (TI) phases, including "higher-order" TIs. However, the 230 SGs only represent a fraction of the 1651 Shubnikov SGs, which characterize the symmetries of both magnetic and non-magnetic crystals. In this talk, we extend TQC to the magnetic Shubnikov SGs (MSGs), forming the complete theory of Magnetic Topological Quantum Chemistry (MTQC). Using MTQC, we construct a complete classification of the magnetic atomic limits [i.e., magnetic Elementary Band Representations (MEBRs)]. Through the MEBRs, we also obtain the little-group corepresentations of the MSGs, complete eigenvalue indicators for strong and fragile magnetic TIs and semimetals, and all possible mean-field band connectivities in crystals with lattice-commensurate magnetism. We introduce new tools on the Bilbao Crystallographic Server for accessing this information, and discuss magnetic topological materials identified using MTQC.