POWER-LAW TEMPERATURE-DEPENDENCE OF THE INELASTIC-SCATTERING RATE IN DISORDERED SUPERCONDUCTORS

We present a theory of the quasiparticle inelastic lifetime tau-in in disordered superconducting films. We find that both the Coulomb and the electron-phonon contribution to tau-in-1 are enhanced by disorder, and that for reasonably strong electron-phonon coupling the latter is dominant. In contrast to clean superconductors, the scattering rate is larger than the recombination rate at all temperatures. This leads to a power-law temperature dependence of tau-in-1, in agreement with experimental observations. The theory quantitatively accounts for the magnitude, disorder dependence, and temperature dependence of tau-in measured in recent experiments.