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Magnetic Topological Quantum Chemistry

ORAL

Abstract

In [Bradlyn et al., Nature (2017)], we introduced Topological Quantum Chemistry (TQC) - a real-space predictive theory of band topology and degeneracy constructed from graph theory and atomic orbitals in the 230 time-reversal- (T-) symmetric space groups (SGs). TQC subsequently fueled the identification of tens of thousands of topological materials, and the discovery of novel topological insulating (TI) phases, including "higher-order" TIs. However, the 230 SGs only represent a fraction of the 1651 Shubnikov SGs, which characterize the symmetries of both magnetic and non-magnetic crystals. In this talk, we extend TQC to the magnetic Shubnikov SGs (MSGs), forming the complete theory of Magnetic Topological Quantum Chemistry (MTQC). Using MTQC, we construct a complete classification of the magnetic atomic limits [i.e., magnetic Elementary Band Representations (MEBRs)]. Through the MEBRs, we also obtain the little-group corepresentations of the MSGs, complete eigenvalue indicators for strong and fragile magnetic TIs and semimetals, and all possible mean-field band connectivities in crystals with lattice-commensurate magnetism. We introduce new tools on the Bilbao Crystallographic Server for accessing this information, and discuss magnetic topological materials identified using MTQC.

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Presenters

  • Benjamin Wieder

    Princeton University, Physics department, Princeton University

Authors

  • Benjamin Wieder

    Princeton University, Physics department, Princeton University

  • Luis Elcoro

    University of the Basque Country, Department of Condensed Matter Physics, University of the Basque Country

  • Zhida Song

    Chinese Academy of Sciences,Institute of Physics, Princeton University, Department of Physics, Princeton University, Physics, Princeton University, Department of Physics, Princeton university, Physics department, Princeton University

  • Yuanfeng Xu

    Max Planck Institute of Microstructure Physics

  • Nicolas Regnault

    Ecole Normale Superieure, Princeton University, Department of Physics, Princeton university, Physics department, Princeton University

  • Barry Bradlyn

    University of Illinois at Urbana-Champaign, Physics, University of Illinois at Urbana-Champaign

  • Andrei Bernevig

    Physics, Princeton University, Princeton Center for Theoretical Science, Princeton University, Princeton University, Department of Physics, Princeton university, Physics department, Princeton University