Numerical investigation of the dynamics of a thin-film type-II superconductor with and without disorder

The equilibrium dynamics of a thin-film type-II superconductor with spherical geometry are investigated numerically in a simulation based on the lowest-Landau-level approximation to the time-dependent Ginzburg-Landau equation. Both the static and time-dependent density-density correlation functions of the superconducting order parameter have been investigated for systems with varying amounts of quenched random disorder. As the temperature is lowered it is found that the correlation length, the length scale over which the vortices have short-range crystalline order, increases but the introduction of quenched random disorder reduces this correlation length. We see no signs of a phase transition in either the pure or the disordered case. For the disordered system there is no evidence for the existence of a Bragg glass phase with quasi-long-range correlations. The dynamics in both the pure and disordered systems is activated, and the barrier of the relaxation mechanism grows linearly with the correlation length. The self-diffusion time scale of the vortices was also measured and has the same temperature dependence as that of the longest time scales found in the time-dependent density-density correlation function. The dominant relaxation mechanism observed is a change in orientation of a correlated region of size of the correlation length. A scaling argument is given to explain the value of the barrier exponent. copyright 1997 The American Physical Society