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Revealing quantum geometry in nonlinear quantum materials.

Yiyang Jiang1,2, Tobias Holder3, Binghai Yan1,2

  • 1Department of Condensed Matter Physics, Weizmann Institute of Science, Rehovot 7610001, Israel.

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|June 13, 2025
PubMed
Summary
This summary is machine-generated.

Quantum geometric quantities, including the metric and connection, are crucial for understanding nonlinear responses in quantum materials. This review connects these quantities to excitation energy, lifetimes, and symmetry, offering new material characterization methods.

Keywords:
Berry curvaturenonlinear conductivityquantum geometryquantum metrictopology

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Area of Science:

  • Condensed matter physics
  • Quantum materials science

Background:

  • Berry curvature has been central to topological phenomena.
  • Quantum geometric quantities like metric and connection were less explored.
  • Nonlinear responses in quantum materials offer new insights.

Purpose of the Study:

  • To provide a modern perspective on quantum geometric quantities in nonlinear responses.
  • To demonstrate the connection between quantum geometry and material properties.
  • To unify the understanding of electron motion beyond linear order.

Main Methods:

  • Reviewing nonlinear optical effects, subgap responses, and nonlinear transport.
  • Analyzing injection and shift currents in the optical regime.
  • Examining quasiparticle lifetimes and their role in subgap responses.

Main Results:

  • Quantum geometric quantities naturally influence nonlinear responses.
  • Resonances in optical regimes are distinguished by quantum geometric quantities.
  • Nonlinear transport reveals anomalous motion linked to Berry curvature and quantum metric dipoles.

Conclusions:

  • Quantum geometry is intimately linked to nonlinear response phenomena.
  • Quantum geometric quantities provide a unified framework for understanding nonlinear effects.
  • This framework enables novel characterization of complex quantum materials.