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Scaling analysis of quantum geometry in second-order nonlinear transport
Zhen-Hao Gong1, Z Z Du2, Hai-Peng Sun3
1State Key Laboratory of Quantum Functional Materials, Department of Physics, Guangdong Provincial Key Laboratory of Topological Matter, and Guangdong Basic Research Center of Excellence for Quantum Science, Southern University of Science and Technology (SUSTech), Shenzhen 518055, China.
Science Bulletin
|August 7, 2026
Summary
Researchers developed a method to distinguish quantum geometry effects from disorder in nonlinear transport measurements. This allows for accurate identification of quantum geometric contributions in experiments.
Area of Science:
- Condensed matter physics
- Quantum mechanics
- Materials science
Background:
- Quantum geometry describes the structure of Hilbert spaces for Bloch states.
- Nonlinear transport measurements can probe quantum geometry.
- Disorder in materials complicates the isolation of quantum-geometric effects.
Purpose of the Study:
- To systematically identify and differentiate quantum geometric and disorder-induced mechanisms contributing to the nonlinear Hall effect.
- To develop a method for quantitative disentanglement of these contributions in experimental data.
Main Methods:
- Systematic enumeration of geometric and disorder-induced mechanisms for the second-order nonlinear Hall effect.
- Derivation of a scaling law relating nonlinear Hall conductivity to linear longitudinal conductivity.
- Analysis of distinct "weight fingerprints" associated with each mechanism.
Main Results:
- A polynomial scaling law was derived for the nonlinear Hall conductivity.
- Each mechanism (geometric or disorder-induced) possesses a unique "weight fingerprint" within this polynomial.
- The method allows for quantitative disentanglement of quantum geometry from disorder, applicable with or without time-reversal symmetry.
Conclusions:
- The derived scaling law and weight fingerprints provide a practical workflow for identifying quantum-geometric contributions in nonlinear transport experiments.
- This work enables clearer experimental observation and understanding of quantum geometry in materials.
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