Time-dependent Ginzburg-Landau equations with charged boundaries

We build a discrete form for the Ginzburg-Landau thermodynamic potential for an infinite film and find how the TDGL equations are related to it. We discuss why the usual superconductor-insulator boundary condition, which prohibits the passage of superconducting current, should be questioned in dynamic problems; nevertheless, we conclude that this condition remains valid. The formalism we develop enables us to deal with situations in which surface charge is present at the boundaries. These situations include the Hall configuration when the influence of the normal electrons is not negligible and the case of an electromagnetic wave parallel to the film. In the case of the electromagnetic wave, we evaluate the electromagnetic field inside the superconductor and follow the motion of the vortices. (c) 2005 American Institute of Physics.