Model for layered superconductors: From Josephson coupling to three-dimensional behavior

We present a model for layered superconductors, where the order parameter between the layers is nonzero, due to proximity effects. In the limit of decoupled layers, this model gives all the terms of the usual Lawrence-Doniach free energy, as well as new terms arising from the existence of an order parameter between the layers. The corresponding Josephson coupling is found to be field dependent. The upper critical field normal to the layers has positive curvature as a function of T, and decreases with increasing interlayer distance, contrary to the predictions of the Lawrence-Doniach model. In addition, the anisotropy deduced from the critical fields ${\mathit{H}}_{\mathit{c}2}$ is markedly different from the low-field anisotropy.