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

The response of a superconductor to the injection of coherent longitudinal phonons is investigated using a Bardeen-Cooper-Schrieffer-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 frequency 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 tau/sub q/ is independent of the energy for T near the critical temperature T/sub c/ is also examined. The solutions of the coupled kinetic equations for the quasiparticle and phonon distribution functions and the energy gap ..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 tau/sub es/ is much shorter than the phonon pair-breaking time tau/sub 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.