Dynamics of the order parameter of superconducting aluminum films

The imaginary part of the pair-field susceptibility of dirty-limit, superconducting, aluminum films has been obtained both above and below the transition temperature by analyzing the I-V characteristic of asymmetric superconducting tunneling junctions. Results obtained above the transition temperature have been found to be consistent with a diffusive time-dependent Ginzburg-Landau equation. Below the transition temperature two modes have been found, one propagating and the other diffusing. The resonant frequency and damping constant of the propagating mode have been compared with the predictions of a phenomenological two-fluid hydrodynamic theory given by Bray and Schmidt. A somewhat more detailed comparison has been made with a microscopic theory given by Schön and Schmid in which the propagating and diffusing modes, respectively, are associated with transverse and longitudinal fluctuations of the order parameter. In both the microscopic and macroscopic theories the propagating mode is a high-frequency superconducting analog of second sound in that it consists of a counter motion of the normal and superfluid.