Giant vortex state in perforated aluminum microsquares

We investigate the nucleation of superconductivity in a uniform perpendicular magnetic field H in aluminum microsquares containing a few (two and four) submicron holes (antidots). The normal/superconducting phase boundary $T_c\mathrm{}\left(H\right)\mathrm{}$ of these structures shows a quite different behavior in low and high fields. In the low magnetic-field regime fluxoid quantization around each antidot leads to oscillations in $T_c\mathrm{}\left(H\right),$ expected from the specific sample geometry, and reminiscent of the network behavior. In high magnetic fields, the $T_c\mathrm{}\left(H\right)\mathrm{}$ boundaries of the perforated and a reference nonperforated microsquare reveal cusps at the same values of $\Phi /{\Phi }_0$ (where $\Phi$ is the applied magnetic flux threading the total square area and ${\Phi }_0$ is the superconducting flux quantum), while the background on $T_c\mathrm{}\left(H\right)\mathrm{}$ becomes quasilinear, indicating that a giant vortex state is established. The influence of the actual geometries on $T_c\mathrm{}\left(H\right)\mathrm{}$ is analyzed in the framework of the linearized Ginzburg-Landau theory.