Josephson Vortices in Weakly-Coupled Superconductors as Topological Solitons of the Sine-Gordon Equations for Phase Differences

• Published in: Journal of low temperature physics 2005-04, Vol.139 (1), p.141-154, Article 141
• Main Author: Kuplevakhsky, Sergey V.
• Format: Article
• Language: English
• ISSN: 0022-2291; 1573-7357
• DOI: 10.1007/s10909-005-3919-y

We present a mathematically rigorous solution of the problem of magnetic properties of weakly-coupled superconducting multilayers with an arbitrary number N not less than 2 of superconducting layers in external parallel magnetic fields H greater than 0. By minimizing a relevant Gibbs free-energy functional, we show that the equilibrium vortex structure is given by a new class of soliton solutions: namely, topological solitons of a system of N - 1 coupled static sine-Gordon equations for the phase differences in a finite spatial interval I = [-L, L]. A complete classification of the new soliton solutions is presented. For N = 2, 3, and N = infinity, exact, closed-form analytical expressions are derived. The special case L = infinity, H = 0 is considered separately. Non-soliton solutions are also analyzed: they are shown to be saddle points of the Gibbs free-energy functional. A comparison with the experiment is drawn.