Problem of Nonlinear Conductivity within Relaxation Time Approximation in Noncentrosymmetric Insulators

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 Phys. Rev. B, 109, L180302 (2024), it is revealed that the RTA has a flaw in predicting finite linear conductivity even for insulators under weak electric fields, and an improved approach based on the Redfield equation is proposed. In this article, it is demonstrated that the RTA also exhibits a flaw in the longitudinal nonlinear DC conductivity for noncentrosymmetric insulators and it is improved by extending the previous approach. This provides a simple alternative to RTA and is expected to be useful for the study of nonlinear and nonequilibrium phenomena.