Stability and transition between vortex configurations in square mesoscopic samples with antidots

Using the complete nonlinear Ginzburg-Landau theory, we investigated the superconducting state and phase boundaries for mesoscopic square samples containing one to four submicron antidots in the presence of a uniform perpendicular magnetic field. The properties of the different vortex states, possible degeneracies, and the transitions between them are studied. Due to the interplay of the different types of symmetry, a qualitative difference in the nucleation of the superconducting state in samples with different number or arrangement of antidots is found. The superconducting/normal state H-T phase boundary of these structures reveals an oscillatory behavior caused by the formation of different stable vortex configurations in these small clusters of pinning centers (antidots). We analyze the stability of these configurations and compare the superconducting phase boundary with experimental results.