Topological solitons of the Lawrence–Doniach model as equilibrium Josephson vortices in layered superconductors
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 Helm...
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Фізико-технічний інститут низьких температур ім. Б.І. Вєркіна НАН України
2004
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| Zitieren: | Topological solitons of the Lawrence–Doniach model as equilibrium Josephson vortices in layered superconductors / S.V. Kuplevakhsky // Физика низких температур. — 2004. — Т. 30, № 7-8. — С. 856-873. — Бібліогр.: 32 назв. — англ. |
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Kuplevakhsky, S.V. 2017-06-10T06:56:47Z 2017-06-10T06:56:47Z 2004 Topological solitons of the Lawrence–Doniach model as equilibrium Josephson vortices in layered superconductors / S.V. Kuplevakhsky // Физика низких температур. — 2004. — Т. 30, № 7-8. — С. 856-873. — Бібліогр.: 32 назв. — англ. 0132-6414 PACS: 74.50.+r, 74.80.Dm, 05.45.Yv https://nasplib.isofts.kiev.ua/handle/123456789/119840 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. en Фізико-технічний інститут низьких температур ім. Б.І. Вєркіна НАН України Физика низких температур Сверхпроводимость и мезоскопические структуры Topological solitons of the Lawrence–Doniach model as equilibrium Josephson vortices in layered superconductors Article published earlier |
| institution |
Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| collection |
DSpace DC |
| title |
Topological solitons of the Lawrence–Doniach model as equilibrium Josephson vortices in layered superconductors |
| spellingShingle |
Topological solitons of the Lawrence–Doniach model as equilibrium Josephson vortices in layered superconductors Kuplevakhsky, S.V. Сверхпроводимость и мезоскопические структуры |
| title_short |
Topological solitons of the Lawrence–Doniach model as equilibrium Josephson vortices in layered superconductors |
| title_full |
Topological solitons of the Lawrence–Doniach model as equilibrium Josephson vortices in layered superconductors |
| title_fullStr |
Topological solitons of the Lawrence–Doniach model as equilibrium Josephson vortices in layered superconductors |
| title_full_unstemmed |
Topological solitons of the Lawrence–Doniach model as equilibrium Josephson vortices in layered superconductors |
| title_sort |
topological solitons of the lawrence–doniach model as equilibrium josephson vortices in layered superconductors |
| author |
Kuplevakhsky, S.V. |
| author_facet |
Kuplevakhsky, S.V. |
| topic |
Сверхпроводимость и мезоскопические структуры |
| topic_facet |
Сверхпроводимость и мезоскопические структуры |
| publishDate |
2004 |
| language |
English |
| publisher |
Фізико-технічний інститут низьких температур ім. Б.І. Вєркіна НАН України |
| format |
Article |
| description |
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.
|
| issn |
0132-6414 |
| url |
https://nasplib.isofts.kiev.ua/handle/123456789/119840 |
| citation_txt |
Topological solitons of the Lawrence–Doniach model as equilibrium Josephson vortices in layered superconductors / S.V. Kuplevakhsky // Физика низких температур. — 2004. — Т. 30, № 7-8. — С. 856-873. — Бібліогр.: 32 назв. — англ. |
| work_keys_str_mv |
AT kuplevakhskysv topologicalsolitonsofthelawrencedoniachmodelasequilibriumjosephsonvorticesinlayeredsuperconductors |
| first_indexed |
2025-11-30T12:47:52Z |
| last_indexed |
2025-11-30T12:47:52Z |
| _version_ |
1850857663359877120 |