Solving the Ginzburg-Landau equations with magnetic translation group

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 Psi 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 less than or similar to B less than or equal to H-c2 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 Hc2.