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

Alama, 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 -