Magnetic topological quantum chemistry

Luis Elcoro, Benjamin J. Wieder, Zhida Song, Yuanfeng Xu, Barry Bradlyn, B. Andrei Bernevig

Research output: Contribution to journalArticlepeer-review

131 Scopus citations


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.

Original languageEnglish (US)
Article number5965
JournalNature communications
Issue number1
StatePublished - Dec 1 2021

All Science Journal Classification (ASJC) codes

  • General Chemistry
  • General Biochemistry, Genetics and Molecular Biology
  • General Physics and Astronomy


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