Magnetic topological quantum chemistry

TLDR

Group‑theoretic characterization of crystalline solids has been foundational for physics and chemistry, yet the theory for crystals with commensurate magnetic order has remained incomplete for decades. This work resolves that long‑standing gap by deriving the small corepresentations, momentum stars, compatibility relations, and magnetic elementary band corepresentations for all 1,421 magnetic space groups, and making them freely available on the Bilbao Crystallographic Server. The authors extend Topological Quantum Chemistry to magnetic space groups, establishing Magnetic Topological Quantum Chemistry (MTQC) as a comprehensive real‑space theory of band topology in both magnetic and nonmagnetic crystals. Applying MTQC, they obtain the full set of symmetry‑based indicators of electronic band topology, revealing symmetry‑respecting bulk states as well as anomalous surface and hinge states.

Abstract

For over 100 years, the group-theoretic characterization of crystalline solids has provided the foundational language for diverse problems in physics and chemistry. However, the group theory of crystals with commensurate magnetic order has remained incomplete for the past 70 years, due to the complicated symmetries of magnetic crystals. In this work, we complete the 100-year-old problem of crystalline group theory by deriving the small corepresentations, momentum stars, compatibility relations, and magnetic elementary band corepresentations of the 1,421 magnetic space groups (MSGs), which we have made freely accessible through tools on the Bilbao Crystallographic Server. We extend Topological Quantum Chemistry to the MSGs to form a complete, real-space theory of band topology in magnetic and nonmagnetic crystalline solids - Magnetic Topological Quantum Chemistry (MTQC). Using MTQC, we derive the complete set of symmetry-based indicators of electronic band topology, for which we identify symmetry-respecting bulk and anomalous surface and hinge states.