Giant vortices in the Ginzburg-Landau description of superconductivity -: art. no. 134512

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 kappa. For n>> 1, they have a simple structure and a free energy F similar ton. In order to relate this behavior to the classic Abrikosov result F similar ton(2) when kappa-->+infinity, we consider the limit where both n>>1 and kappa >> 1, and obtain a scaling function of the variable kappa /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 kappa of a giant vortex.