Magnetic Topological Quantum Chemistry
Abstract
Over the last 100 years, the grouptheoretic characterization of crystalline solids has provided the foundational language for diverse problems in physics and chemistry. There exist two classes of crystalline solids: nonmagnetic crystals left invariant by space groups (SGs), and solids with commensurate magnetic order that respect the symmetries of magnetic space groups (MSGs). Whereas many of the properties of the SGs, such as their momentumspace corepresentations (coreps) and elementary band coreps (EBRs) were tabulated with relative ease, progress on deriving the analogous properties of the MSGs has largely stalled for the past 70 years due to the complicated symmetries of magnetic crystals. In this work, we complete the 100yearold problem of crystalline group theory by deriving the small coreps, momentum stars, compatibility relations, and magnetic EBRs (MEBRs) of the single (spinless) and double (spinful) MSGs. We have implemented freelyaccessible tools on the Bilbao Crystallographic Server for accessing the coreps of the MSGs, whose wideranging applications include neutron diffraction investigations of magnetic structure, the interplay of lattice regularization and (symmetryenhanced) fermion doubling, and magnetic topological phases, such as axion insulators and spin liquids. Using the MEBRs, we extend the earlier theory of Topological Quantum Chemistry to the MSGs to form a complete, realspace theory of band topology in magnetic and nonmagnetic crystalline solids  Magnetic Topological Quantum Chemistry (MTQC). We then use MTQC to derive the complete set of symmetrybased indicators (SIs) of band topology in all spinful (fermionic) crystals, for which we identify symmetryrespecting bulk and anomalous surface and hinge states. Lastly, using the SIs, we discover several novel nonaxionic magnetic higherorder topological insulators.
 Publication:

arXiv eprints
 Pub Date:
 October 2020
 arXiv:
 arXiv:2010.00598
 Bibcode:
 2020arXiv201000598E
 Keywords:

 Condensed Matter  Mesoscale and Nanoscale Physics;
 Condensed Matter  Strongly Correlated Electrons;
 Mathematical Physics
 EPrint:
 8 pg main text + 181 pg appendix, 4 + 25 figures, abstract abridged for arXiv posting  see paper for full abstract, previously submitted