Penetration of the magnetic field into a 3D ordered Josephson medium at very small values of the pinning parameter

Abstract

The Meissner state of a 3D Josephson medium is analyzed for stability against small fluctuations of phase discontinuities at contacts. For any form of fluctuations, there exists value I ₀ of pinning parameter I such that the Meissner configuration remains stable if I < I ₀. Reasons why the configuration remains stable at small I are considered. Instability arises when the quadratic form of the second variation of Gibbs potential G is not a positively definite quantity. At small I, the contribution of the Josephson energy to G is small. The second variation of the magnetic energy, the other component of G, is always a positively definite quadratic form. Therefore, instability may arise only if I has a finite value. This statement holds true not only for the Meissner but also for any equilibrium configuration. At I < I ₀, stability persists up to the boundary of the Meissner state. Then, a sequence of plane vortices parallel to the boundary appears throughout the sample. Thus, vortices appearing at I < I ₀ are plane vortices rather than linear. The configurations of currents and the magnetic field profile inside the sample are calculated for I < I ₀. Calculation is based on analyzing the continuous variation of the current configuration toward a decrease in the Gibbs potential.