Magnetic topological quantum chemistry

Elcoro Cengotitabengoa, Luis Angel; Wieder, Benjamin J.; Song, Zhi-Da; Xu, Yuan-Feng; Bradlyn, Barry; Bernevig, B. Andrei

dc.contributor.author	Elcoro Cengotitabengoa, Luis Angel
dc.contributor.author	Wieder, Benjamin J.
dc.contributor.author	Song, Zhi-Da
dc.contributor.author	Xu, Yuan-Feng
dc.contributor.author	Bradlyn, Barry
dc.contributor.author	Bernevig, B. Andrei
dc.date.accessioned	2021-11-12T09:30:57Z
dc.date.available	2021-11-12T09:30:57Z
dc.date.issued	2021-10-13
dc.identifier.citation	Nature Communications 12 : (2021) // Article ID 5965	es_ES
dc.identifier.issn	2041-1723
dc.identifier.uri	http://hdl.handle.net/10810/53741
dc.description.abstract	[EN]The band topology of nonmagnetic crystals can be characterized by Topological Quantum Chemistry (TQC), whereas the band topology of magnetic crystals remains unexplored. Here, the authors extend TQC to the magnetic space groups to form a complete, real-space theory of band topology in magnetic and nonmagnetic crystalline solids. 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.	es_ES
dc.description.sponsorship	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.	es_ES
dc.language.iso	eng	es_ES
dc.publisher	Nature Research	es_ES
dc.relation	info:eu-repo/grantAgreement/MICINN/PID2019-106644GB-I00	es_ES
dc.rights	info:eu-repo/semantics/openAccess	es_ES
dc.rights.uri	http://creativecommons.org/licenses/by/3.0/es/	*
dc.subject	bilbao crystallographic server	es_ES
dc.subject	phase	es_ES
dc.subject	semimetal	es_ES
dc.subject	representations	es_ES
dc.subject	discovery	es_ES
dc.subject	fermions	es_ES
dc.subject	catalog	es_ES
dc.subject	parity	es_ES
dc.subject	states	es_ES
dc.subject	point	es_ES
dc.title	Magnetic topological quantum chemistry	es_ES
dc.type	info:eu-repo/semantics/article	es_ES
dc.rights.holder	This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made. The images or other third party material in this article are included in the article’s Creative Commons license, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons license and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this license, visit http://creativecommons.org/licenses/by/4.0/.	es_ES
dc.rights.holder	Atribución 3.0 España	*
dc.relation.publisherversion	https://www.nature.com/articles/s41467-021-26241-8	es_ES
dc.identifier.doi	10.1038/s41467-021-26241-8
dc.departamentoes	Física	es_ES
dc.departamentoeu	Fisika	es_ES

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This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made. The images or other third party material in this article are included in the article’s Creative Commons license, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons license and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this license, visit http://creativecommons.org/licenses/by/4.0/.

Except where otherwise noted, this item's license is described as This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made. The images or other third party material in this article are included in the article’s Creative Commons license, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons license and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this license, visit http://creativecommons.org/licenses/by/4.0/.