Vortex entry conditions in type-II superconductors. Effect of surface defects

The conditions for the vortex entry into type-II superconductors being in the mixed state, are studied by means of both numerical and analytical solution of the Ginzburg-Landau equations. A modulation instability of the superconducting order parameter is shown to occur when the kinematic momentum (or supervelocity) of the condensate reaches a threshold value at the superconductor edge or surface. Due to this instability, vortices start to nucleate at the edge/surface and then penetrate deeper into the sample. It is found that the presence of surface defects causes a noticeable drop of the first penetration field and leads to a qualitative change of the magnetization curve. Based on these results a simple phenomenological model of the edge or surface barrier, taking into account the effect of surface defects, is suggested