Giant vortices in the Ginzburg-Landau description of superconductivity

Abstract

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 $n\gg 1$, they have a simple structure and a free energy $\mathcal{F}\sim n$. In order to relate this behaviour to the classic Abrikosov result $\mathcal{F}\sim n^2$ when $\kappa \to +\infty$, we consider the limit where both $n\gg 1$ and $\kappa \gg 1$, and obtain a scaling function of the variable $\kappa /n$ that describes the cross-over between these two behaviours of $\mathcal{F}$. 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.

35 pages, 10 figures

References in corpus (2)

• Transitions between different superconducting states in mesoscopic disks
• A dual point description of mesoscopic superconductors

Cited by in corpus (2)

• The London Study of Vortex States in a Superconducting Film Due to a Magnetic Dot
• Giant vortices in small mesoscopic disks: an approximate description