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arXiv · 2410.04995

Scaling analysis of quantum geometry in second-order nonlinear transport

Zhen-Hao Gong·Z. Z. Du·Hai-Peng Sun·Hai-Zhou Lu·X. C. Xie
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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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Zhen-Hao Gong, Z. Z. Du, Hai-Peng Sun, Hai-Zhou Lu, X. C. Xie. 2024-10-07. Scaling analysis of quantum geometry in second-order nonlinear transport. https://arxiv.org/abs/2410.04995

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