Gauge invariance of excitonic linear and nonlinear optical response

Abstract

Excitons strongly influence the optical response of low-dimensional materials. Here, the authors propose a practical framework for calculating the excitonic linear and nonlinear optical response of multiband semiconductors based on the perturbative density matrix within the mean-field approximation. Using this framework, the equivalence of four different approaches is demonstrated analytically and numerically, if the correct velocity gauge interaction is used. The four approaches stem from two choices of gauge and two ways of computing the response functions. The present formalism can readily be extended to generate gauge invariant responses for higher-order nonlinear processes.