Nonlinear Correction to Absorption Spectrum under Irradiation of Microwave Field in Conventional BCS Superconductors

Abstract

We investigate the absorption spectrum of s-wave superconductors under microwave pump field irradiation. The third-order response function is calculated in the dirty limit with the electron–phonon interaction included at finite temperatures. We find that the nonlinear correction to the linear absorption shows peculiar behavior when the pump field frequency is smaller than the superconducting gap. At finite temperatures, a negative nonlinear correction exists, which is caused by thermally excited quasiparticles. The vertex correction by impurity scattering is found to contain a dissipation mechanism by inelastic scattering (interaction between electrons and acoustic phonons) or nonlocality. We need this mechanism to obtain finite absorption in a nonequilibrium stationary state under a monochromatic external field. Although this term originates from the deformation of a one-particle state, there is also a final-state interaction (the amplitude mode). The latter term represents two-photon excitation and is a...