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Updated: Aug 9, 2026

Scalable Quantum Integrated Circuits on Superconducting Two-Dimensional Electron Gas Platform
Published on: August 2, 2019
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.
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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