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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

On the shape of interlayer vortices in the Lawrence-Doniach model


Authors: Stan Alama, Lia Bronsard and Etienne Sandier
Journal: Trans. Amer. Math. Soc. 360 (2008), 1-34
MSC (2000): Primary 35J50, 58J37
Published electronically: August 6, 2007
MathSciNet review: 2341992
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Abstract: We consider the Lawrence-Doniach model for layered superconductors, in which stacks of parallel superconducting planes are coupled via the Josephson effect. To model experiments in which the superconductor is placed in an external magnetic field oriented parallel to the superconducting planes, we study the structure of isolated vortices for a doubly periodic problem. We consider a singular limit which simulates certain experimental regimes in which isolated vortices have been observed, corresponding to letting the interlayer spacing of the superconducting planes tend to zero and the Ginzburg-Landau parameter $ \kappa\to\infty$ simultaneously, but at a fixed relative rate.


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Additional Information

Stan Alama
Affiliation: Department of Mathematics and Statistics, McMaster University, Hamilton, Ontario, Canada L8S 4K1

Lia Bronsard
Affiliation: Department of Mathematics and Statistics, McMaster University, Hamilton, Ontario, Canada L8S 4K1

Etienne Sandier
Affiliation: Departement des Mathématiques, Université Paris XII, 64 avenue du Général de Gaulle, 94010 Créteil Cedex, France

DOI: http://dx.doi.org/10.1090/S0002-9947-07-04188-8
PII: S 0002-9947(07)04188-8
Keywords: Calculus of variations, elliptic equations and systems, superconductivity, vortices.
Received by editor(s): March 8, 2004
Received by editor(s) in revised form: June 16, 2005
Published electronically: August 6, 2007
Additional Notes: The first and second authors were supported by an NSERC Research Grant
Article copyright: © Copyright 2007 American Mathematical Society