Giant vortices in small mesoscopic disks: an approximate description

We present an approximate description of the giant vortex state in a thin mesoscopic superconducting disk within the phenomenological Ginzburg-Landau approach. Analytical asymptotic expressions for the energies of the states with fixed vorticity are obtained when a small magnetic flux is accumulated in the disk. The spectrum of the lowest Landau levels of such a disk is also discussed.