Superheating of the Meissner State and the Giant Vortex State of a Cylinder of Finite Extent

The superheating field and the size-dependent critical field of the Meissner state for a cylinder of radius $R$, with Ginzburg-Landau (GL) parameters $\kappa$ between 0.3 and 2.4 and size parameters $\frac{R}{\lambda }$ between 2.5 and 20, have been calculated from the GL theory. For very large values of $\frac{R}{\lambda }$ the superheating field of the cylinder approaches that of the semi-infinite half-space. Similiar studies of the giant vortex state show that the superheating fields are smaller than for the Meissner state. Under certain conditions, as the applied magnetic field is increased, the solutions to the GL equations may cease to exist for the Meissner and giant vortex state for a constant value of the fluxoid quantum number before the Gibbs free energy of the superconducting state reaches that of the normal state.