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We analyze theoretically and experimentally vortex configurations inmesoscopic superconducting squares. Our theoretical approach is based on theanalytical solution of the London equation using Green's-function method. Thepotential-energy landscape found for each vortex configuration is then used inLangevin-type molecular-dynamics simulations to obtain stable vortexconfigurations. Metastable states and transitions between them and the groundstate are analyzed. We present our results of the first direct visualization ofvortex patterns in micrometer-sized Nb squares, using the Bitter decorationtechnique. We show that the filling rules for vortices in squares withincreasing applied magnetic field can be formulated, although in a differentmanner than in disks, in terms of formation of vortex "shells".

Vortex states in mesoscopic superconducting squares: Formation of vortex shells