Josephson current in an anisotropic d-wave model

There should be no Josephson current between a CuO2 plane with a gap of dx2-y2 symmetry and a conventional s-wave superconductor. Nevertheless such a current is observed to exist between YBa2Cu3O7 (YBCO) and Pb although with a reduced magnitude. Penetration depth measurements have revealed a large anisotropy between a and b directions presumably due to the existence of the CuO chains. Using a simple anisotropic tight-binding model in qualitative agreement with the measured penetration depths and a standard model for the spin susceptibility, we obtain, on solution of the BCS gap equations, a gap function with mainly dx2-y2 symmetry but with a minor extended s-wave component. The resultant Josephson current for YBCO-Pb junctions is in good agreement with experiment.