Topological solitons of the Lawrence-Doniach model as equilibrium Josephson vortices in layered superconductors

Сверхпроводимость и мезоскопические структуры

Автор(и)

  • Sergey V. Kuplevakhsky B. Verkin Institute for Low Temperature Physics and Engineering of the National Academy of Science of Ukraine, 47 Lenin Ave., Kharkov 61103, Ukraine

DOI:

https://doi.org/10.1063/1.1789938

Ключові слова:

PACS: 74.50. r, 74.80.Dm, 05.45.Yv

Анотація

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.

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Опубліковано

2004-06-17

Як цитувати

(1)
Kuplevakhsky, S. V. Topological Solitons of the Lawrence-Doniach Model As Equilibrium Josephson Vortices in Layered Superconductors: Сверхпроводимость и мезоскопические структуры. Fiz. Nizk. Temp. 2004, 30, 856-8.

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