Nonlinear response functions and disorder: The case of the photogalvanic effect

We investigate the impact of disorder in the form of impurity scattering on a generalized version of the circular photogalvanic effect (CPGE) in Weyl semimetals where the frequency detuning between the two orthogonally polarized beams is nonzero. Considering a minimal model with two Weyl nodes at different energies, we employ the self-consistent Born approximation to unravel the dependence of the associated two-point retarded Green's function on the strength of intra- and internode scattering, frequency detuning, and energy difference between the two Weyl nodes. In the case of intranode scattering only, the second-order current density acquires Drude-like features, which we elucidate further by introducing an effective scattering strength. The Drude-like theory can even describe the second-order response in the presence of strong internode scattering, provided the latter has a linear interdependence with the intranode scattering. By properly adjusting the frequency detuning, we also find the real part of the two-point retarded Green's function to be reminiscent of a “quantized CPGE”-like form, although the imaginary part of the latter function is in general finite, and the second-order current density oscillates with time due to the finite frequency detuning. We finally conclude with an outlook on possible experimental consequences.