Non-Axionic Magnetic Higher-Order Topological Insulators and High-Throughput Magnetic Topological Materials Discovery from Magnetic Topological Quantum Chemistry

In [Bradlyn*, Elcoro*, Cano*, Vergniory*, Wang*, et al., Nature (2017)], we introduced Topological Quantum Chemistry (TQC) - a real-space predictive theory of band topology in nonmagnetic crystals. TQC subsequently fueled the successful identification of tens of thousands of topological materials, and the discovery of novel topological insulating (TI) phases. This past year, we have completed the 70-year-old problem of group theory in magnetic crystals, facilitating the formulation of a complete position-space theory of band topology in magnetic solids - Magnetic Topological Quantum Chemistry (MTQC) [Elcoro*, Wieder*, et al., arXiv:2010.00598 (2020)]. Through MTQC, we have derived the complete symmetry-based indicators of spinful magnetic band topology, discovered novel exceptions to symmetry-enhanced fermion doubling theorems, and uncovered the existence of magnetic TIs with response theories beyond axion electrodynamics. We have additionally employed MTQC to perform the first high-throughput search for magnetic topological materials [Xu, et al., Nature (2020)], discovering over 100 magnetic TIs and semimetals with experimentally established magnetic structures.