Critical current density limited by the surface barrier in thin films with the magnetic field-parallel to the surface

The vortex pinning due to the Bean-Livingston surface barrier in the superconducting slabs is considered within the framework of the London theory, and a simple expression of the critical current density is derived. The surface barrier is effective especially in thin films which has the thickness less than the penetration depth and high critical current density no less than those due to the bulk pinning, when an external magnetic field is applied parallel to the film surface. The resulting critical current density has the logarithmic field dependence, and is inversely proportional to the thickness of the slab. These results show good agreement with the existing observed data for NbTi films, and are applied to the data for YBaCuO films.<>