Problem of nonlinear conductivity within relaxation time approximation in noncentrosymmetric insulators

TL;DR

This paper examines the limitations of the relaxation time approximation in predicting nonlinear conductivity in noncentrosymmetric insulators and proposes an improved approach for studying nonlinear nonequilibrium phenomena.

Contribution

The authors extend their improved approach to nonlinear responses, offering a simple alternative to the traditional RTA for analyzing nonlinear and nonequilibrium effects.

Findings

RTA predicts finite linear conductivity in insulators under weak fields, which is flawed.

An improved approach based on the Redfield equation addresses this flaw.

The new method simplifies the analysis of nonlinear and nonequilibrium phenomena.

Abstract

With the recent advancements in laser technology, there has been increasing interest in nonlinear and nonperturbative phenomena such as nonreciprocal transport, the nonlinear Hall effect, and nonlinear optical responses. When analyzing the nonequilibrium steady state, the relaxation time approximation (RTA) in the quantum kinetic equation has been widely used. However, recent studies have highlighted problems with the use of RTA that require careful consideration. In a study published in Phys. Rev. B, $\textbf{109}$, L180302 (2024), we revealed that the RTA has a flaw in predicting finite linear conductivity even for insulators under weak electric fields, and improved the RTA based on the Redfield equation. In this paper, we further extend our approach to nonlinear responses. This approach provides a simple alternative to RTA and is expected to be useful for the study of nonlinear and nonequilibrium phenomena.