Flux penetration and expulsion in thin superconducting disks

The saddle points of the free energy separating the stable states with a different number of vortices are obtained numerically. In contrast to known surface and geometrical barrier models, we find that in a wide range of magnetic fields below the penetration field, the saddle point state for flux penetration into a disk does not correspond to a vortex located near the sample boundary, but to a region of suppressed superconductivity at the disk edge with no winding of the current, and which is a nucleus for the following vortex creation. The height of this nucleation barrier, which determines the time of flux penetration, is calculated for different disk radii and magnetic fields.