Non commensurate vortex lattices in a composite antidot lattice or dc current

Within the phenomenological Ginzburg-Landau theory we investigate the effect of a composite antidot lattice and small dc applied current to the stability of commensurate and non commensurate vortex structures in perforated type-II superconducting samples in the weak pinning regime. We found that a composite antidot lattice, consisting of small and big antidots in the unit cell, considerably increases the probability to find square pinned vortex lattice as compared to a sample with a regular square array of antidots. An applied current also favors the square pinned vortex states. These results indicate that both the applied current and a composite pinning array distort the broad local minimum in the free energy which keeps the vortices away from the pinning centers.