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Updated: Aug 10, 2025
08:55
Methods of Ex Situ and In Situ Investigations of Structural Transformations: The Case of Crystallization of Metallic Glasses
Published on: June 7, 2018
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Classification of time-reversal-invariant crystals with gauge structures
Z Y Chen1, Zheng Zhang1, Shengyuan A Yang2
1National Laboratory of Solid State Microstructures and Department of Physics, Nanjing University, 210093, Nanjing, China.
Nature Communications
|February 10, 2023
Summary
This study unifies the theory of projective representations for crystal symmetries, classifying 458 algebras. It reveals three physical signatures, enabling new topological states in artificial crystals.
Area of Science:
- Condensed Matter Physics
- Quantum Mechanics
- Crystallography
Background:
- Quantum states can exhibit projective representations of symmetries, crucial for understanding crystals.
- Projective representations of space groups are vital for artificial crystals but lack a unified theory.
Purpose of the Study:
- To establish a unified theory for projective symmetry algebras in time-reversal-invariant crystals.
- To classify and represent all projective symmetry algebras for 17 wallpaper groups in 2D.
Main Methods:
- Exhaustive classification of 458 projective symmetry algebras.
- Representation of these algebras for 2D time-reversal-invariant crystals.
Main Results:
- Identified 189 algebraically non-equivalent projective symmetry algebras.
- Discovered three physical signatures: shifted high-symmetry momenta, nontrivial Zak phase, and a spinless eight-fold nodal point.
Conclusions:
- Provides a theoretical foundation for artificial crystals and projective symmetry.
- Opens avenues for novel topological states and phenomena beyond current paradigms.
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