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Quantum geometry in condensed matter
Tianyu Liu1,2, Xiao-Bin Qiang3,4, Hai-Zhou Lu3,4
1International Quantum Academy, Shenzhen 518048, China.
National Science Review
|February 17, 2025
Summary
Quantum geometry, including Berry curvature and quantum metric, profoundly influences condensed matter properties. This review details its impact on nonlinear transport, superconductivity, and topological states.
Area of Science:
- Condensed matter physics
- Quantum mechanics
- Geometric phases
Background:
- Modern physics describes nature using geometry.
- Electron motion in condensed matter relates to Hilbert space geometry.
- Quantum geometry encompasses Berry curvature and quantum metric.
Purpose of the Study:
- To review the role of quantum geometry in condensed matter.
- To highlight its effects on material properties.
- To explore future research directions.
Main Methods:
- Review of theoretical concepts and experimental findings.
- Analysis of quantum geometry's influence on material properties.
Main Results:
- Quantum geometry, via Berry curvature and quantum metric, drives nonlinear transport.
- The quantum metric enhances superconductivity transition temperatures in flat bands.
- Uniform momentum-space quantum geometry stabilizes fractional Chern insulators, leading to the fractional quantum anomalous Hall effect.
Conclusions:
- Quantum geometry is crucial for understanding nonlinear transport, superconductivity, and topological phenomena in materials.
- Further research into quantum geometry promises new discoveries in condensed matter physics.
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