Scaling analysis of quantum geometry in second-order nonlinear transport
arXiv:2410.04995
The paper derives a scaling law that separates quantum‑geometric contributions from disorder effects in the second‑order nonlinear Hall response, allowing experimental identification of quantum geometry in transport measurements.
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.
8 pages, 3 figures, 4 tables