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Magnetic topological quantum chemistry

Author

Listed:
  • Luis Elcoro

    (University of the Basque Country UPV/EHU)

  • Benjamin J. Wieder

    (Massachusetts Institute of Technology
    Northeastern University
    Princeton University)

  • Zhida Song

    (Princeton University)

  • Yuanfeng Xu

    (Max Planck Institute of Microstructure Physics)

  • Barry Bradlyn

    (University of Illinois at Urbana-Champaign)

  • B. Andrei Bernevig

    (Princeton University
    Donostia International Physics Center
    IKERBASQUE, Basque Foundation for Science)

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.

Suggested Citation

  • Luis Elcoro & Benjamin J. Wieder & Zhida Song & Yuanfeng Xu & Barry Bradlyn & B. Andrei Bernevig, 2021. "Magnetic topological quantum chemistry," Nature Communications, Nature, vol. 12(1), pages 1-10, December.
    • Handle: RePEc:nat:natcom:v:12:y:2021:i:1:d:10.1038_s41467-021-26241-8
    DOI: 10.1038/s41467-021-26241-8
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    References listed on IDEAS

    as
    1. Barry Bradlyn & L. Elcoro & Jennifer Cano & M. G. Vergniory & Zhijun Wang & C. Felser & M. I. Aroyo & B. Andrei Bernevig, 2017. "Topological quantum chemistry," Nature, Nature, vol. 547(7663), pages 298-305, July.
    2. Tiantian Zhang & Yi Jiang & Zhida Song & He Huang & Yuqing He & Zhong Fang & Hongming Weng & Chen Fang, 2019. "Catalogue of topological electronic materials," Nature, Nature, vol. 566(7745), pages 475-479, February.
    3. Feng Tang & Hoi Chun Po & Ashvin Vishwanath & Xiangang Wan, 2019. "Comprehensive search for topological materials using symmetry indicators," Nature, Nature, vol. 566(7745), pages 486-489, February.
    4. M. G. Vergniory & L. Elcoro & Claudia Felser & Nicolas Regnault & B. Andrei Bernevig & Zhijun Wang, 2019. "A complete catalogue of high-quality topological materials," Nature, Nature, vol. 566(7745), pages 480-485, February.
    5. Hoi Chun Po & Ashvin Vishwanath & Haruki Watanabe, 2017. "Symmetry-based indicators of band topology in the 230 space groups," Nature Communications, Nature, vol. 8(1), pages 1-9, December.
    Full references (including those not matched with items on IDEAS)

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    Cited by:

    1. Jonah Herzog-Arbeitman & B. Andrei Bernevig & Zhi-Da Song, 2024. "Interacting topological quantum chemistry in 2D with many-body real space invariants," Nature Communications, Nature, vol. 15(1), pages 1-9, December.
    2. Kuan-Sen Lin & Giandomenico Palumbo & Zhaopeng Guo & Yoonseok Hwang & Jeremy Blackburn & Daniel P. Shoemaker & Fahad Mahmood & Zhijun Wang & Gregory A. Fiete & Benjamin J. Wieder & Barry Bradlyn, 2024. "Spin-resolved topology and partial axion angles in three-dimensional insulators," Nature Communications, Nature, vol. 15(1), pages 1-17, December.
    3. Frank Schindler & Stepan S. Tsirkin & Titus Neupert & B. Andrei Bernevig & Benjamin J. Wieder, 2022. "Topological zero-dimensional defect and flux states in three-dimensional insulators," Nature Communications, Nature, vol. 13(1), pages 1-18, December.

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