Nonlinear Response of Diffusive Superconductors to $ac$-electromagnetic Fields

Abstract

Motivated by the recent experimental progress in studying conventional and unconventional superconductors in a pump-probe setup, we perform a comprehensive theoretical analysis of the nonlinear response of a diffusive BCS conventional superconductor to the action of an alternating electromagnetic field using a generalized Usadel equation. We analyze the response up to the second order of the perturbation in the amplitude of the vector potential $\vec{A}$, the superconducting order parameter $\Delta$ and in the third order for the current $\vec{j}$. On the basis of this approach, we derive general expressions for the retarded (advanced) Green's functions, as well as the Keldysh function for an arbitrary number of harmonics of the incident field. Most importantly, we analyze the set of physical observables in a non-equilibrium superconductor, such as frequency and the temperature dependencies of the zero harmonic $\delta (\Delta {)}_0$ (Eliashberg effect), the second harmonic $\delta (\Delta {)}_{2\Omega }$, as well as the third harmonic for the electric current $j(3\Omega )$ under the action of a monochromatic irradiation. For the same set of parameters, we also analyze the behavior of the reflectivity and the down-conversion intensity of a thin superconducting film, discussed recently in the context of parametric amplification of superconductivity. We derive these quantities microscopically and show the connection of the down-conversion intensity to the third harmonic generation currents induced by the amplitude mode and the direct action of the electric field on the charge carriers.

16 pages, 8 figures, typos are corrected, further details of the derivations are added

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Cited by in corpus (8)

• Quantum geometry induced microwave enhancement of flat band superconductivity
• Spatially resolved collective modes in d-wave superconductors
• Two-dimensional coherent spectroscopy of disordered superconductors in the narrow-band and broad-band limits
• Nonequilibrium nonlinear response theory of amplitude-dependent dissipative conductivity in disordered superconductors
• Optical Pumping of Bardeen-Cooper-Schrieffer Superconductors
• Optical conductivity of a dirty current-carrying superconductor
• Hybrid collective excitations in topological superconductor/ferromagnetic insulator heterostructures
• Third-harmonic generation in superconductors: Role of quantum geometry in the competition between Higgs mode and quasiparticles