Pair-field susceptibility of superconducting Al-Er films

Measurements of the imaginary part of the pair-field susceptibility χ″ have been carried out on dirty-limit superconducting Al films doped with Er impurities at temperatures within 20% of the critical temperature T_c. These studies are the first measurements of χ″ (Ω, k) as a function of the pair-breaking parameter ρ{variant}. Samples exhibiting values of ρ{variant} up to 0.1 were studied. At temperatures above T_c the diffusive time-dependent Ginzburg-Landau equation for order-parameter fluctuations was found to be valid in the presence of pair-breaking, with the Ginzburg-Landau time an increasing function of the pair-breaking, in quantitative agreement with theory. The characteristic frequencies of the transverse and longitudinal modes of the order parameter disequilibrium were determined from the measurements of χ″ (Ω, k) below T_c by fitting to a functional form which exhibits the essential features of the most detailed theories, in particular those of Orbach and Entin-Wohlman, Dinter, and Schön and Ambegaokar, The propagating charge-imbalance wave was found to be overdamped for large values of ρ{variant}, consistent with the theory of the transverse mode in the presence of finite pair-breaking. The peak in the excess current found near the gap voltage appears to be due to a resonance in the longitudinal mode pair-field susceptibility and not the result of single-particle tunneling as previously suggested by šimanek and Hayward. The width of this resonance as derived by Schön and Ambegaokar for the gap regime is equal to the reciprocal of the spin-flip scattering time. The other characteristic feature of the pair-field susceptibility is the peak associated with the longitudinal mode, which occurs at a frequency which is a measure of the relaxation of the amplitude of the order parameter. Dinter's theory, in particular, describes the dependence of the width of this peak on the pair-breaking parameter ρ{variant}.