Vortices in a long periodically modulated Josephson contact containing a few magnetic flux quanta

Abstract

The possibility of existence of vortices containing a few magnetic flux quanta in a long periodically ordered Josephson contact is investigated. The computer algorithm is proposed, which makes it possible to calculate exactly any symmetric current configuration containing vortices of only one direction. The variants of an approximate analytic approach and of an exact computer calculation are considered. The values of the pinning parameter, for which the corresponding solutions exist for the cases of 2, 3, and 4 flux quanta, are calculated. It is shown that vortex energy is a quadratic function of the number of flux quanta in it. The stability of the found configurations to small fluctuations of phase jumps is analyzed. It is shown that at reasonably large values of I, stable solutions of any configuration can exist (in particular, with any number of quanta in a cell). At the beginning of each range of values of I, in which a corresponding solution exists, there is an interval (sometimes very small) in which the solution is unstable.