Topological solitons of the Lawrence–Doniach model as equilibrium Josephson vortices in layered superconductors - Kuplevakhsky, S.V. (Фізико-технічний інститут низьких температур ім. Б.І. Вєркіна НАН України, 2004)
We present a complete, exact solution of the problem of the magnetic properties of layered superconductors
with an infinite number of superconducting layers in parallel fields H 0. Based on
a new exact variational method, we determine the type of all stationary points of both the Gibbs
and Helmholtz free-energy functionals. For the Gibbs free-energy functional, they are either
points of strict, strong minima or saddle points. All stationary points of the Helmholtz free-energy
functional are those of strict, strong minima. The only minimizes of both the functionals are the
Meissner (0-soliton) solution and soliton solutions. The latter represent equilibrium Josephson
vortices. In contrast, non-soliton configurations (interpreted in some previous publications as
«isolated fluxons» and «fluxon lattices») are shown to be saddle points of the Gibbs free-energy
functional: They violate the conservation law for the flux and the stationarity condition for the
Helmholtz free-energy functional. For stable solutions, we give a topological classification and establish
a one-to-one correspondence with Abrikosov vortices in type-II superconductors. In the
limit of weak interlayer coupling, exact, closed-form expressions for all stable solutions are derived:
They are nothing but the «vacuum state» and topological solitons of the coupled static
sine-Gordon equations for the phase differences. The stable solutions cover the whole field range
0 < H < ∞ and their stability regions overlap. Soliton solutions exist for arbitrary small transverse
dimensions of the system, provided the field H to be sufficiently high. Aside from their importance
for weak superconductivity, the new soliton solutions can find applications in different fields of
nonlinear physics and applied mathematics.