# On the Lawrence–Doniach model of superconductivity: magnetic fields parallel to the axes

Stan Alama; Lia Bronsard; Etienne Sandier

Journal of the European Mathematical Society (2012)

- Volume: 014, Issue: 6, page 1825-1857
- ISSN: 1435-9855

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topAlama, Stan, Bronsard, Lia, and Sandier, Etienne. "On the Lawrence–Doniach model of superconductivity: magnetic fields parallel to the axes." Journal of the European Mathematical Society 014.6 (2012): 1825-1857. <http://eudml.org/doc/277588>.

@article{Alama2012,

abstract = {We consider periodic minimizers of the Lawrence–Doniach functional, which models highly anisotropic superconductors with layered structure, in the simultaneous limit as the layer thickness tends to zero and the Ginzburg–Landau parameter tends to infinity. In particular, we consider the properties of minimizers when the system is subjected to an external magnetic field applied either tangentially or normally to the superconducting planes. For normally applied fields, our results show that the resulting "pancake" vortices will be vertically aligned. In horizontal fields we show that there are two-parameter regimes in which minimizers exhibit very different characteristics. The low-field regime resembles the Ginzburg–Landau model, while the high-field limit gives a "transparent state" described in the physical literature. To obtain our results we derive sharp matching upper and lower bounds on the global minimizers of the energy.},

author = {Alama, Stan, Bronsard, Lia, Sandier, Etienne},

journal = {Journal of the European Mathematical Society},

keywords = {calculus of variations; elliptic equations and systems; superconductivity; vortices; calculus of variations; elliptic equations and systems; superconductivity; vortices},

language = {eng},

number = {6},

pages = {1825-1857},

publisher = {European Mathematical Society Publishing House},

title = {On the Lawrence–Doniach model of superconductivity: magnetic fields parallel to the axes},

url = {http://eudml.org/doc/277588},

volume = {014},

year = {2012},

}

TY - JOUR

AU - Alama, Stan

AU - Bronsard, Lia

AU - Sandier, Etienne

TI - On the Lawrence–Doniach model of superconductivity: magnetic fields parallel to the axes

JO - Journal of the European Mathematical Society

PY - 2012

PB - European Mathematical Society Publishing House

VL - 014

IS - 6

SP - 1825

EP - 1857

AB - We consider periodic minimizers of the Lawrence–Doniach functional, which models highly anisotropic superconductors with layered structure, in the simultaneous limit as the layer thickness tends to zero and the Ginzburg–Landau parameter tends to infinity. In particular, we consider the properties of minimizers when the system is subjected to an external magnetic field applied either tangentially or normally to the superconducting planes. For normally applied fields, our results show that the resulting "pancake" vortices will be vertically aligned. In horizontal fields we show that there are two-parameter regimes in which minimizers exhibit very different characteristics. The low-field regime resembles the Ginzburg–Landau model, while the high-field limit gives a "transparent state" described in the physical literature. To obtain our results we derive sharp matching upper and lower bounds on the global minimizers of the energy.

LA - eng

KW - calculus of variations; elliptic equations and systems; superconductivity; vortices; calculus of variations; elliptic equations and systems; superconductivity; vortices

UR - http://eudml.org/doc/277588

ER -

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