Layered superconductivity models at the London limit and their continuum properties

We write the London limit of the Lawrence Doniach free energy in terms of the local magnetic field and of the average supercurrent over the interplane distance. Starting from this formulation we study a model where the supercurrent at the buffer layers is obtained from the superconducting sheets by a Taylor expansion. The continuum limit of this model gives corrections to the anisotropic London theory due to the layered structure.