Vortex dynamics, pinning, and critical currents in a Ginzburg-Landau type-II superconductor

The dynamics of vortices in a type-II superconductor with defects are studied by solving the time-dependent Ginzburg-Landau equations in two and three dimensions. We show that vortex flux tubes are trapped by volume defects up to a critical current density where they begin to jump between pinning sites along static flow channels. We study the dependence of the critical current on the pinning distribution and find for random distributions a maximum critical current equal to a few percent of the depairing current at a pinning density three times larger than the vortex line density. Whereas for a regular triangular pinning array, the critical current is significantly larger when the pinning density matches the vortex line density.