Zu Abrikosovs Theorie der periodischen Lösungen der GL-Gleichungen für Supraleiter 2. Art

Abstract

Abrikosov's method to get periodic solutions of the GL-equations for superconductors of type II is reformulated in order to make higher approximations possible. It is shown that instead of the external magnetic field, the average field in the superconductor must be used as fixed quantity in the approximations; then the method can be extended to a general iteration procedure with a fixed period-parallelogram for the solution. In the first approximation every periodic solution is given by a simple product of ϑ-functions; among those solutions which possess one flux quantum per period-parallelogram only, the hexagonal modification has the lowest free energy as already proposed byKleiner et al.