Solving the Ginzburg-Landau Equations with Magnetic Translation Group

Abstract

This paper presents a powerful method to obtain flux-lattice solutions of the Ginzburg-Landau equations in any external field. A key point lies in expanding the order parameter Ψ in a basis consisting of the eigenstates of the magnetic translation operators in the mean flux density B . It is shown that retaining a few terms in the expansion provides practically exact solutions over \(0 \lesssim B \leq H_{{\rm c}2}\). Abrikosov's result near H c2 is obtained here as a lowest-order approximation. The method clarifies how the higher-Landau-level mixing grows as the field is decreased from H c2 .