Kinetic equation study of phonon-induced nonequilibrium states in superconducting films

Abstract

The response of a superconductor to the injection of coherent longitudinal phonons is investigated using a Bardeen-Cooper-Schrieffer- (BCS-) type energy-gap equation and the coupled nonlinear quasiparticle and phonon kinetic equations of Chang and Scalapino. The superconductor is assumed to be a weak-coupling, isotropic film which is perturbed in a spatially uniform steady-state manner. The frequently used quasiparticle relaxation-time theory of Eliashberg is first used to study the effects associated with changing the temperature $T$ and with changing the frequency and strength of the phonon field. The effect of assuming that the quasiparticle relaxation time ${\ensuremath{\tau}}_{q}$ is independent of the energy for $T$ near the critical temperature ${T}_{c}$ is also examined. The solutions of the coupled kinetic equations for the quasiparticle and phonon distribution functions and the energy gap $\ensuremath{\Delta}(T)$ are then presented and compared to the results obtained from the relaxation-time model. It is seen that even for low-power absorption levels the relaxation-time model is valid only when the phonon escape time ${\ensuremath{\tau}}_{\mathrm{es}}$ is much shorter than the phonon pair-breaking time ${\ensuremath{\tau}}_{B}$. The experimental data of Tredwell and Jacobsen and their theoretical calculations using the relaxation-time model are briefly discussed in the light of these results.