Identifying geometric third-order nonlinear transport in disordered materials
arXiv:2510.24239 · doi:10.1103/515g-qjq8
The paper presents a symmetry‑guided framework to separate quantum‑geometric and disorder‑mediated contributions to third‑order nonlinear transport in disordered materials, using magnetic point‑group diagnostics and scaling relations between nonlinear Hall and linear conductivities, and demonstrates its use on various 2D, topological and altermagnetic systems.
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.
10 pages, 3 figures, 2 table