  Bogoliubov-de Gennes theory is used to investigate the effect of the size of
a superconducting square on the vortex states in the quantum confinement
regime. When the superconducting coherence length is comparable to the Fermi
wavelength, the shape resonances of the superconducting order parameter have
strong influence on the vortex configuration. Several unconventional vortex
states, including asymmetric ones, giant multi-vortex combinations, and states
comprising giant antivortex, were found as ground states and their stability
was found to be very sensitive on the value of $k_F\xi_0$, the size of the
sample $W$, and the magnetic flux $\Phi$. By increasing the temperature and/or
enlarging the size of the sample, quantum confinement is suppressed and the
conventional mesoscopic vortex states as predicted by the Ginzburg-Laudau (GL)
theory are recovered. However, contrary to the GL results we found that the
states containing symmetry-induced vortex-antivortex pairs are stable over the
whole temperature range. It turns out that the inhomogeneous order parameter
induced by quantum confinement favors vortex-antivortex molecules, as well as
giant vortices with a rich structure in the vortex core - unattainable in the
GL domain.

Superconductivity