PERIODIC VORTEX LATTICES FOR THE LAWRENCE–DONIACH MODEL OF LAYERED SUPERCONDUCTORS IN A PARALLEL FIELD

Author:

ALAMA S.1,BRONSARD L.1,BERLINSKY A. J.2

Affiliation:

1. Department of Mathematics and Statistics, McMaster University, Hamilton, Ontario, Canada L8S 4K1, Canada

2. Department of Physics and Astronomy, McMaster University, Hamilton, Ontario, Canada L8S 4K1, Canada

Abstract

We consider the Lawrence–Doniach model for layered superconductors, in which stacks of parallel superconducting planes are coupled via the Josephson effect. We assume that the superconductor is placed in an external magnetic field oriented parallel to the superconducting planes and study periodic lattice configurations in the limit as the Josephson coupling parameter r→0. This limit leads to the "transparent state" discussed in the physics literature, which is observed in very anisotropic high-Tc superconductors at sufficiently high applied fields and below a critical temperature. We use a Lyapunov–Schmidt reduction to prove that energy minimization uniquely determines the geometry of the optimal vortex lattice: a period-2 (in the layers) array proposed by Bulaevskiĭ & Clem. Finally, we discuss the apparent conflict with previous results for finite-width samples, in which the minimizer in the small coupling regime takes the form of "vortex planes" (introduced by Theodorakis and Kuplevakhsky).

Publisher

World Scientific Pub Co Pte Lt

Subject

Applied Mathematics,General Mathematics

Cited by 6 articles. 订阅此论文施引文献 订阅此论文施引文献,注册后可以免费订阅5篇论文的施引文献,订阅后可以查看论文全部施引文献

1. Analysis of minimizers of the Lawrence-Doniach energy for superconductors in applied fields;Discrete & Continuous Dynamical Systems - B;2017

2. Minimizers of the Lawrence–Doniach Functional with Oblique Magnetic Fields;Communications in Mathematical Physics;2012-01-07

3. On the Lawrence–Doniach model of superconductivity: magnetic fields parallel to the axes;Journal of the European Mathematical Society;2012

4. ON MATHEMATICAL MODELS FOR BOSE–EINSTEIN CONDENSATES IN OPTICAL LATTICES;Reviews in Mathematical Physics;2009-03

5. On the shape of interlayer vortices in the Lawrence--Doniach model;Transactions of the American Mathematical Society;2008-01-01

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