Identifying geometric third-order nonlinear transport in disordered materials

TL;DR

This paper develops a comprehensive theory to distinguish geometric quantum effects from disorder scattering in third-order nonlinear transport, enabling identification of specific mechanisms in various quantum materials.

Contribution

The authors introduce a theory that treats geometric effects and disorder scattering equally, deriving a scaling law to identify geometric mechanisms of third-order nonlinear transport.

Findings

Identified 20 mechanisms of third-order nonlinear transport.

Derived a polynomial scaling law linking nonlinear Hall conductivity and longitudinal conductivity.

Applied the theory to various materials, including 2D and topological materials.

Abstract

In third-order nonlinear transport, a voltage can be measured in response to the cube of a driving current as a result of the quantum geometric effects, which has attracted tremendous attention. However, in realistic materials where disorder scattering also contributes to nonlinear transport, identifying the geometric mechanisms remains a challenge. We find a total of 20 mechanisms of third-order nonlinear transport by developing a comprehensive theory that treats the geometric effects and disorder scattering on an equal footing. More importantly, we find that 12 of these mechanisms can be unambiguously identified, by deriving a scaling law that expresses the third-order nonlinear Hall conductivity as a polynomial in the linear longitudinal conductivity. We apply this theory to identify the geometric mechanisms of third-order nonlinear transport in materials both with and without time-reversal symmetry, such as 2D materials, topological materials, and altermagnets. This theory further promotes nonlinear transport as a probe of geometric effects and phase transitions in quantum materials.