Giant vortices in the Ginzburg-Landau description of superconductivity

Recent experiments on mesoscopic samples and theoretical considerations lead us to analyze multiply charged (n>1) vortex solutions of the Ginzburg-Landau equations for arbitrary values of the Landau-Ginzburg parameter κ. For n≫1, they have a simple structure and a free energy F∼n. In order to relate this behavior to the classic Abrikosov result F∼n₂ when κ→ + ∞, we consider the limit where both n≫1 and κ≫1, and obtain a scaling function of the variable κ/n that describes the crossover between these two behaviors of F. It is then shown that a small-n expansion can also be performed and the first two terms of this expansion are calculated. Finally, large and small n expansions are given for recently computed phenomenological exponents characterizing the free energy growth with κ of a giant vortex.