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Bogoliubov-de Gennes theory is used to investigate the effect of the size ofa superconducting square on the vortex states in the quantum confinementregime. When the superconducting coherence length is comparable to the Fermiwavelength, the shape resonances of the superconducting order parameter havestrong influence on the vortex configuration. Several unconventional vortexstates, including asymmetric ones, giant multi-vortex combinations, and statescomprising giant antivortex, were found as ground states and their stabilitywas found to be very sensitive on the value of $k_F\xi_0$, the size of thesample $W$, and the magnetic flux $\Phi$. By increasing the temperature and/orenlarging the size of the sample, quantum confinement is suppressed and theconventional mesoscopic vortex states as predicted by the Ginzburg-Laudau (GL)theory are recovered. However, contrary to the GL results we found that thestates containing symmetry-induced vortex-antivortex pairs are stable over thewhole temperature range. It turns out that the inhomogeneous order parameterinduced by quantum confinement favors vortex-antivortex molecules, as well asgiant vortices with a rich structure in the vortex core - unattainable in theGL domain.

Vortex states in nanoscale superconducting squares: the influence of quantum confinement