Nonlinear electromagnetic response and Higgs-mode excitation in BCS superconductors with impurities

Recently, light-induced excitation of Higgs modes, i.e., oscillations of the order-parameter amplitude in superconductors, has been observed. The mechanism of this effect has remained not fully understood. In the absence of relaxation processes, the order-parameter amplitude is not affected by the irradiation, since the systems of quasiparticle excitations and Cooper pairs move together and remain in equilibrium with each other. This work demonstrates how the relaxation of quasiparticles by impurity scattering leads to finite coupling between the Higgs mode and light. The suggested theory can be used to study light-matter interaction in anisotropic and multiband superconductors, such as high-temperature cuprates, iron pnictides, and magnesium diboride.