Giant vortex state in mesoscopic superconductors

Using the self-consistent solution of the nonlinear Ginzburg-Landau equations, the superconducting state of a type II mesoscopic cylinder and of an infinite thin sheet with a circular hole (antidot), in the presence of an homogeneous magnetic field is studied. Close to the third critical field, the magnetic field penetrates the sample in the form of a vortex around the axis of the cylinder or of the antidot. This result has been found previously by other authors. The vortex, called a giant vortex, can carry several flux quanta. The giant vortex is persistent when the state is metastable and evolves to the so called paramagnetic Meissner effect (PME) within the cylinder. The behaviour of this effect as a function of the Ginzburg-Landau (GL) parameter is studied and the results are discussed. Gibbs free energy, order parameter and magnetic induccion as a function of the applied field and of the GL parameter are also studied.