Strong-coupling theory of the interlayer tunnelling 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 interactions. The equations for the superconducting transition temperature Tc are solved numerically for several models of electron - optical phonon coupling. The nonmagnetic in-plane impurity scattering suppresses the Tc in all cases considered, and it is possible to obtain a fair agreement with experiments for a reasonable choice of parameters. For the anisotropic electron - phonon coupling proposed by Song and Annett we find that the interlayer pair tunnelling can stabilize the dx2-y2-wave superconducting state with a high Tc. Moreover, in this case there is a possibility of impurity-induced crossover from the dx2-y2-wave state stabilized by the interlayer tunnelling to the s-wave state at a low impurity concentration. We also calculate the isotope effect associated 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 that give high transition temperatures. (author)