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We consider periodic minimizers of the LawrenceDoniach functional, which models highly anisotropic superconductors with layered structure, in the simultaneous limit as the layer thickness tends to zero and the GinzburgLandau 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 GinzburgLandau 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.

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