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Scaling analysis of quantum geometry in second-order nonlinear transport

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arxiv 2410.04995 v4 pith:IZ7XPXNS submitted 2024-10-07 cond-mat.mes-hall cond-mat.mtrl-scicond-mat.other

Zhen-Hao Gong , Z. Z. Du , Hai-Peng Sun , Hai-Zhou Lu , X. C. Xie This is my paper · ORCID
classification cond-mat.mes-hallcond-mat.mtrl-scicond-mat.other
keywords nonlineargeometryquantumtransportconductivitycontributionsdisorder-inducedexperiments
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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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Cited by 5 Pith papers

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  1. Fundamental Relations as the Leading Order in Nonlinear Thermoelectric Responses with Time-Reversal Symmetry

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    Disorder-induced second-order transport in TRS topological insulators obeys Mott-type and Wiedemann-Franz-type relations with a universal side-jump coefficient -L/3 and a Coulomb-screening-dependent skew-scattering co...

  2. Sliding-tuned Quantum Geometry in Moir\'e Systems: Nonlinear Hall Effect and Quantum Metric Control

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  3. Nonlinear spin-Seebeck diode in $f$-wave magnets, third-order spin-Nernst effects in $g$-wave magnets and spin-Nernst effects in $i$-wave altermagnets

    cond-mat.mes-hall 2026-02 conditional novelty 5.0 of 10

    A Boltzmann-equation calculation predicts second-order spin-Seebeck currents in f-wave magnets, third-order spin-Nernst currents in g-wave magnets, and linear spin-Nernst currents in i-wave altermagnets, all without s...

  4. Electro-optic Kerr Effect Induced by Nonlinear Transport in monolayer WTe2

    cond-mat.other 2025-07 reject novelty 5.0 of 10

    A theoretical prediction that a Berry-curvature-dipole-driven Kerr rotation in monolayer WTe2 can serve as a time-resolved optical probe of the nonlinear Hall effect.

  5. Quantum Geometry Phenomena in Condensed Matter Systems

    cond-mat.str-el 2025-08 conditional novelty 2.0 of 10

    Quantum geometry, especially the quantum metric, is surveyed as a unifying framework for a wide range of transport and optical phenomena, with experimental confirmation in several materials.

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