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Magnetic topological quantum chemistry.

Luis Elcoro1, Benjamin J Wieder2,3,4, Zhida Song5

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Summary
This summary is machine-generated.

This study completes 100-year-old crystalline group theory by deriving magnetic space groups (MSGs) and developing Magnetic Topological Quantum Chemistry (MTQC) for band topology in magnetic crystals.

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Area of Science:

  • Solid-state physics
  • Quantum chemistry
  • Materials science

Background:

  • Group theory has long characterized crystalline solids.
  • The group theory of magnetic crystals remained incomplete for 70 years due to complex symmetries.
  • This gap hindered the full understanding of magnetic materials' electronic properties.

Purpose of the Study:

  • To complete the 100-year-old problem of crystalline group theory for magnetic crystals.
  • To develop a comprehensive theory for electronic band topology in both magnetic and nonmagnetic solids.
  • To provide tools for identifying topological states in materials.

Main Methods:

  • Derived small corepresentations, momentum stars, and compatibility relations for 1,421 magnetic space groups (MSGs).
  • Extended Topological Quantum Chemistry to MSGs, creating Magnetic Topological Quantum Chemistry (MTQC).
  • Developed symmetry-based indicators for electronic band topology.

Main Results:

  • Completed the group-theoretic characterization of magnetic crystals.
  • Made MSG data and tools accessible via the Bilbao Crystallographic Server.
  • Identified symmetry-respecting bulk and anomalous surface/hinge states using MTQC.

Conclusions:

  • MTQC provides a complete, real-space theory of band topology for crystalline solids.
  • The derived indicators enable the classification and prediction of topological electronic states.
  • This work facilitates the discovery of novel quantum materials with tailored electronic properties.