Scaling Law for Time-Reversal-Odd Nonlinear Transport

TL;DR

This paper derives a comprehensive scaling law for time-reversal-odd nonlinear transport, revealing how disorder scattering influences the nonlinear conductivity, which is crucial for understanding experimental observations.

Contribution

It introduces a general scaling law accounting for multiple scattering sources, clarifying the role of extrinsic contributions in $ au$-odd nonlinear transport.

Findings

Nonlinear conductivity is a quartic function of $\sigma_{xx}$.

Extrinsic scattering contributions can dominate the intrinsic response.

Zeroth order extrinsic terms are explicitly demonstrated in a Dirac model.

Abstract

Time-reversal-odd ($\mathcal{T}$-odd) nonlinear current response has been theoretically proposed and experimentally confirmed recently. However, the role of disorder scattering in the response, especially whether it contributes to the $\sigma_{xx}$-independent term, has not been clarified. In this work, we derive a general scaling law for this effect, which accounts for multiple scattering sources. We show that the nonlinear conductivity is generally a quartic function in $\sigma_{xx}$. Besides intrinsic contribution, extrinsic contributions from scattering also enter the zeroth order term, and their values can be comparable to or even larger than the intrinsic one. Terms beyond zeroth order are all extrinsic. Cubic and quartic terms must involve skew scattering and they signal competition between at least two scattering sources. The behavior of zeroth order extrinsic terms is explicitly demonstrated in a Dirac model. Our finding reveals the significant role of disorder scattering in $\mathcal{T}$-odd nonlinear transport, and establishes a foundation for analyzing experimental result.