TY - JOUR
T1 - Magnetic topological quantum chemistry
AU - Elcoro, Luis
AU - Wieder, Benjamin J.
AU - Song, Zhida
AU - Xu, Yuanfeng
AU - Bradlyn, Barry
AU - Bernevig, B. Andrei
N1 - Funding Information:
We thank Mois I. Aroyo, Jennifer Cano, Claudia Felser, Nicolas Regnault, Maia G. Vergniory, and Zhijun Wang for crucial discussions during the early stages of this project. B.J.W., B.B., and B.A.B. acknowledge the hospitality of the Donostia International Physics Center, where parts of this work were carried out. The analytic calculations performed for this work were supported by the Department of Energy Grant No. DE-SC0016239. B.J.W., Z.S., and B.A.B. were further supported by NSF EAGER Grant No. DMR 1643312, NSF-MRSEC Grant Nos. DMR-2011750 and DMR-142051, Simons Investigator Grant No. 404513, ONR Grant Nos. N00014-14-1-0330 and N00014-20-1-2303, the Packard Foundation, the Schmidt Fund for Innovative Research, the BSF Israel US Foundation Grant No. 2018226, the Gordon and Betty Moore Foundation through Grant No. GBMF8685 towards the Princeton theory program, and a Guggenheim Fellowship from the John Simon Guggenheim Memorial Foundation. L. E. was supported by the Government of the Basque Country (Project IT1301-19) and the Spanish Ministry of Science and Innovation (PID2019-106644GB-I00). L.E. and B.A.B. acknowledge additional support through the ERC Advanced Grant Superflat, and Y.X. and B.A.B. received additional support from the Max Planck Society. B.B. acknowledges the support of the Alfred P. Sloan Foundation and the National Science Foundation Grant No. DMR-1945058. Concurrently with the preparation of this work, the theory of MTQC was employed to perform a high-throughput search for magnetic topological materials81. Additionally, after the submission of this work, the authors of ref.82 used the group theory of magnetic spin space groups to analyze topological phases in crystals with commensurate magnetic order and negligible spin-orbit coupling. Lastly, after the submission of this work, the authors of ref.83 computed the complete topological crystal constructions of all gapped spinful topological phases in all 1,421 double MSGs, related the resulting topological crystals to the magnetic SIs in each MSG, and deduced the spinful SISM phases in each MSG. We have confirmed complete agreement between the calculations performed in ref.83 and the magnetic SIs and topological phases introduced in this work.
Publisher Copyright:
© 2021, The Author(s).
PY - 2021/12/1
Y1 - 2021/12/1
N2 - 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.
AB - 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.
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U2 - 10.1038/s41467-021-26241-8
DO - 10.1038/s41467-021-26241-8
M3 - Article
C2 - 34645841
AN - SCOPUS:85117368456
SN - 2041-1723
VL - 12
JO - Nature Communications
JF - Nature Communications
IS - 1
M1 - 5965
ER -