Time-dependent Ginzburg-Landau equations for mixed and s-wave superconductors

A set of coupled time-dependent Ginzburg-Landau equations (TDGL) for superconductors of mixed (Formula presented) and s-wave symmetry are derived microscopically from the Gor’kov equations by using the analytical continuation technique. The scattering effects due to impurities with both nonmagnetic and magnetic interactions are considered. We find that the (Formula presented) and s-wave components of the order parameter can have very different relaxation times in the presence of nonmagnetic impurities. This result is contrary to a set of phenomenologically proposed TDGL equations and thus may lead to new physics in the dynamics of flux motion.