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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| Дата: | 2004 |
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| Автор: | |
| Формат: | Стаття |
| Мова: | English |
| Опубліковано: |
Фізико-технічний інститут низьких температур ім. Б.І. Вєркіна НАН України
2004
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| Назва видання: | Физика низких температур |
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| Онлайн доступ: | http://dspace.nbuv.gov.ua/handle/123456789/119840 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Цитувати: | 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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irk-123456789-1198402017-06-11T03:05:13Z Topological solitons of the Lawrence–Doniach model as equilibrium Josephson vortices in layered superconductors Kuplevakhsky, S.V. Сверхпроводимость и мезоскопические структуры 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. 2004 Article 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 http://dspace.nbuv.gov.ua/handle/123456789/119840 en Физика низких температур Фізико-технічний інститут низьких температур ім. Б.І. Вєркіна НАН України |
| institution |
Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| collection |
DSpace DC |
| language |
English |
| topic |
Сверхпроводимость и мезоскопические структуры Сверхпроводимость и мезоскопические структуры |
| spellingShingle |
Сверхпроводимость и мезоскопические структуры Сверхпроводимость и мезоскопические структуры Kuplevakhsky, S.V. Topological solitons of the Lawrence–Doniach model as equilibrium Josephson vortices in layered superconductors Физика низких температур |
| 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. |
| format |
Article |
| author |
Kuplevakhsky, S.V. |
| author_facet |
Kuplevakhsky, S.V. |
| author_sort |
Kuplevakhsky, S.V. |
| title |
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_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 |
| publisher |
Фізико-технічний інститут низьких температур ім. Б.І. Вєркіна НАН України |
| publishDate |
2004 |
| topic_facet |
Сверхпроводимость и мезоскопические структуры |
| url |
http://dspace.nbuv.gov.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. |
| series |
Физика низких температур |
| work_keys_str_mv |
AT kuplevakhskysv topologicalsolitonsofthelawrencedoniachmodelasequilibriumjosephsonvorticesinlayeredsuperconductors |
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2023-10-18T20:35:33Z |
| last_indexed |
2023-10-18T20:35:33Z |
| _version_ |
1796150603032821760 |