Paraconductivity in nonuniform Josephson junctions

The Time Dependent Ginzburg-Landau equation is believed to describe the dynamics of the fluctuating order parameter of superconductors operated above their superconducting transition temperature, T/sub c/. In this theory the relaxation rate of the fluctuating order parameter is a linear function of temperature T for T greater than or equal to T/sub c/. However, recent experiments utilizing pair tunneling in Al--Al2O3--Pb junctions to directly measure the order parameter relaxation rate have indicated suppression of the relaxation rate from linearity over a temperature region much larger than the Ginzburg critical region. In order to explain this behavior two possible mechanisms are presented: First, the effect of random variations of the junction barrier thickness is calculated assuming Gaussian statistics and a Gaussian correlation function for the spatial variation in barrier thickness. Variations in thickness of root mean square amplitude of 1 A and wavelength of 18,000 A are needed to explain the data. Second, the effect of static fluctuations of the local T/sub c/ of the aluminum film on the dynamic order parameter is calculated in the Gaussian approximation. Fluctuations of average size approximately equal to the correlation length and mean square amplitude approximately 0.058 give good agreement with the experimental data