Inverse Faraday effect in superconductors with potential impurities

I consider a nonlinear response of conventional superconductors contaminated with nonmagnetic impurities or imperfections to a circular polarized light. I focus on dc contributions to the induced current density which describe the emergence of the static magnetization in a superconductor. This effect is known as inverse Faraday effect. By employing quasiclassical theory of superconductivity, I derive an expression for the induced static magnetization as a function of frequency of external ac field and disorder scattering rate. The scattering of electrons off potential impurities is taken into account within the framework of the self-consistent Born approximation. It is found that the magnitude of the inverse Faraday effect decreases with an increase in disorder scattering rate. I have also discovered that the value of the induced magnetization has a characteristic minimum at a frequency which approximately equals twice the value of the pairing gap in a clean superconductor. This minimum appears due to the resonant excitation of the amplitude Higgs mode.