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Peer-reviewedCC BY中国科学通报：英文版

Scaling analysis of quantum geometry in second-order nonlinear transport

  • Zhen-Hao Gong1
  • Zhihong Du2
  • Hai-Peng Sun3
  • Hai‐Zhou Lu
  • X. C. Xie4
4 affiliations
  1. 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
  2. 2State 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; Quantum Science Center of Guangdong-Hong Kong-Macao Greater Bay Area (Guangdong), Shenzhen 518045, China
  3. 3Shenzhen Key Laboratory of Ultraintense Laser and Advanced Material Technology, Center for Intense Laser Application Technology, and College of Engineering Physics, Shenzhen Technology University, Shenzhen 518118, China
  4. 4Interdisciplinary Center for Theoretical Physics and Information Sciences (ICTPIS), Fudan University, Shanghai 200433, China; International Center for Quantum Materials, School of Physics, Peking University, Beijing 100871, China; Hefei National Laboratory, Hefei 230088, China
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Abstract

Quantum geometry encodes the structure of the Hilbert space of Bloch states and can be accessed through nonlinear transport. Yet, disorder-induced mechanisms generically contribute to nonlinear transport, making it difficult to isolate quantum-geometric contributions in experiments. Here we systematically enumerate geometric and disorder-induced mechanisms of the second-order nonlinear Hall effect and derive a scaling law that expresses the nonlinear Hall conductivity as a polynomial of the linear longitudinal conductivity. Crucially, each mechanism carries a distinct "weight fingerprint" in the polynomial, enabling a quantitative disentanglement of quantum geometry from disorder backgrounds in existing experiments, both with and without time-reversal symmetry. Our results provide an implementable workflow for identifying quantum-geometric contributions in nonlinear-transport measurements.

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Cite

BibTeXRIS
BibTeX
@article{gong2026scaling,
  title = {{Scaling analysis of quantum geometry in second-order nonlinear transport}},
  author = {Zhen-Hao Gong and Zhihong Du and Hai-Peng Sun and Hai‐Zhou Lu and X. C. Xie},
  journal = {中国科学通报：英文版},
  year = {2026},
  month = jul,
  doi = {10.1016/j.scib.2026.07.062},
  url = {https://doi.org/10.1016/j.scib.2026.07.062},
  note = {CC BY},
}
RIS
TY  - JOUR
TI  - Scaling analysis of quantum geometry in second-order nonlinear transport
AU  - Zhen-Hao Gong
AU  - Zhihong Du
AU  - Hai-Peng Sun
AU  - Hai‐Zhou Lu
AU  - X. C. Xie
PY  - 2026
DA  - 2026/07/27
JO  - 中国科学通报：英文版
DO  - 10.1016/j.scib.2026.07.062
UR  - https://doi.org/10.1016/j.scib.2026.07.062
AB  - Quantum geometry encodes the structure of the Hilbert space of Bloch states and can be accessed through nonlinear transport. Yet, disorder-induced mechanisms generically contribute to nonlinear transport, making it difficult to isolate quantum-geometric contributions in experiments. Here we systematically enumerate geometric and disorder-induced mechanisms of the second-order nonlinear Hall effect and derive a scaling law that expresses the nonlinear Hall conductivity as a polynomial of the linear longitudinal conductivity. Crucially, each mechanism carries a distinct "weight fingerprint" in the polynomial, enabling a quantitative disentanglement of quantum geometry from disorder backgrounds in existing experiments, both with and without time-reversal symmetry. Our results provide an implementable workflow for identifying quantum-geometric contributions in nonlinear-transport measurements.
SN  - 2095-9273
SN  - 2095-9281
ER  -