Geometrical surface vortex pinning in superconducting films

A model is proposed for vortex pinning in a superconducting film with a rough surface. The model relates the critical current to the steepness of the surface relief and, at a high vortex concentration, to the distance between neighboring steepness maxima on the paths of vortex motion. The dependence of the critical current density on the thickness of a high-$T_c$ superconducting film is measured in a weak magnetic field. Its behavior can be explained by the pinning at the stepped surface relief.