Magnetic Topological Quantum Chemistry

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.

arXiv commentFinal version, 10 pg main text + 184 pg appendix, 5 + 25 figures

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• Structure and Topology of Band Structures in the 1651 Magnetic Space Groups
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• Spin-group symmetry in magnetic materials with negligible spin-orbit coupling
• Strong and Fragile Topological Dirac Semimetals with Higher-Order Fermi Arcs
• Real Space Invariants: Twisted Bulk-Boundary Correspondence of Fragile Topology
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• Realizing topological surface states in a lower-dimensional flat band
• A 1d lattice model for the boundary of the quantum spin-Hall insulator

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• Consecutive topological phase transitions and colossal magnetoresistance in a magnetic topological semimetal
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• Intrinsic Magnetic Topological Materials
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• Symmetry-adapted models for multifold fermions with spin-orbit coupling
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