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...
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| Date: | 2004 |
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| Format: | Article |
| Language: | English |
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Фізико-технічний інститут низьких температур ім. Б.І. Вєркіна НАН України
2004
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| Online Access: | https://nasplib.isofts.kiev.ua/handle/123456789/119840 |
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| Journal Title: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Cite this: | 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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Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862632371602325504 |
|---|---|
| author | Kuplevakhsky, S.V. |
| author_facet | Kuplevakhsky, S.V. |
| 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. |
| collection | DSpace DC |
| 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.
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| first_indexed | 2025-11-30T12:47:52Z |
| format | Article |
| fulltext | |
| id | nasplib_isofts_kiev_ua-123456789-119840 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 0132-6414 |
| language | English |
| last_indexed | 2025-11-30T12:47:52Z |
| publishDate | 2004 |
| publisher | Фізико-технічний інститут низьких температур ім. Б.І. Вєркіна НАН України |
| record_format | dspace |
| spelling | 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 |
| spellingShingle | Topological solitons of the Lawrence–Doniach model as equilibrium Josephson vortices in layered superconductors Kuplevakhsky, S.V. Сверхпроводимость и мезоскопические структуры |
| title | 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_short | 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 |
| topic | Сверхпроводимость и мезоскопические структуры |
| topic_facet | Сверхпроводимость и мезоскопические структуры |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/119840 |
| work_keys_str_mv | AT kuplevakhskysv topologicalsolitonsofthelawrencedoniachmodelasequilibriumjosephsonvorticesinlayeredsuperconductors |