STRONG-COUPLING THEORY OF THE INTERLAYER TUNNELING MODEL FOR HIGH-TEMPERATURE SUPERCONDUCTORS

The interlayer pair tunnelling model of Anderson et al is generalized to include the strong-coupling effects associated with in-plane intera ctions. The equations for the superconducting transition temperature T -c are solved numerically for several models of electron-optical phono n coupling. The nonmagnetic in-plane impurity scattering suppresses th e T-c in all cases considered, and it is possible to obtain a fair agr eement with experiments for a reasonable choice of parameters. For the anisotropic electron-phonon coupling proposed by Song and Annett we f ind that the interlayer pair tunnelling can stabilize the d(x2-y2)-wav e superconducting state with a high T-c. Moreover, in this case there is a possibility of impurity-induced crossover from the d(x2-y2)-wave state stabilized by the interlayer tunnelling to the s-wave state at a low impurity concentration. We also calculate the isotope effect asso ciated with the in-plane oxygen optical mode and its dependence on the strength of the interlayer pair tunnelling. Small positive values of the isotope exponent are obtained for strengths of pair tunnelling tha t give high transition temperatures.