Variational method applied to two-component Ginzburg-Landau theory

Abstract

In this paper, we apply a variational method to two-component superconductors, as in the MgB2 materials, using the two-component Ginzburg-Landau (GL) theory. We expand the order parameter in a series of eigenfunctions containing one or two terms in each component. We also assume azimuthal symmetry to the set of eigenfunctions used in the mathematical procedure. The extension of the GL theory to two components leads to the quantization of the magnetic flux in fractions of ϕ0. We consider two kinds of component interaction potentials: Γ1|ΨI|2|ΨII|2 and \documentclass[12pt]{minimal}\begin{document}$\Gamma _2(\Psi _I^*\Psi _{II}+\Psi _I\Psi _{II}^*)$\end{document}Γ2(ΨI*ΨII+ΨIΨII*). The simplicity of the method allows one to implement it in a broad range of physical systems, such as hybrid magnetic-superconducting mesoscopic systems, texturized thin films, metallic hydrogen superfluid, and mesoscopic superconductors near inhomogeneous magnetic fields, simply by replacing the vector potential by its corresponding expression. As an example, we apply our results to a disk of radius R and thickness t.