Coupled two-dimensional Fermi liquids as a model for layered superconductors: Basic equations and elementary results

We develop a microscopic model of layered superconductors, designed specifically for the high-${\mathit{T}}_{\mathit{c}}$ cuprates, which is valid at all temperatures below the degeneracy temperature and for all relevant length scales. The model is based on the original idea of Bulaevskii, and consists of a stack of two-dimensional conducting planes coupled via interlayer diffusion of charge carriers. The microscopic model presented here reduces to the phenomenological Ginzburg-Landau, Lawrence-Doniach, and anisotropic London models in the appropriate limits. We derive the main equations of the interlayer diffusion model, then use the model to examine the role of dimensionality and interlayer scattering on the magnetic properties of layered superconductors.