BCS versus Josephson pair hopping between theCuO2layers in high-Tcsuperconductors

We start with the two-dimensional (2D) scattering matrix for two electrons of opposite spin and momentum, accounting for the fluctuating pair correlations in a single ${\mathrm{CuO}}_2$ layer, and consider the interlayer pair hopping by (a) BCS scattering out of the layer and (b) Josephson tunneling between layers. The experimental 3D transition temperature $T_c$ is found as a function of the interlayer BCS coupling parameter and the Josephson-tunneling matrix element. We discuss the relative importance of both of these transfer mechanisms for the Y and Tl compounds.