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

DOI:
https://doi.org/10.1090/S0002-9947-07-04188-8

Published electronically:
August 6, 2007

MathSciNet review:
2341992

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Abstract | References | Similar Articles | Additional Information

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 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:
https://doi.org/10.1090/S0002-9947-07-04188-8

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