c-axis Josephson tunneling in twinned and untwinned YBCO-Pb Junctions

Within a microscopic two-band model of planes and chains with a pairing potential in the planes and off-diagonal pairing between planes and chains we find that the chains make the largest contribution to the Josephson tunneling current and that through them the d-wave part of the gap contributes to the current. This is contrary to the usual assumption that the d-wave part of the gap does not contribute to the c-axis Josephson current for incoherent tunneling into an s-wave superconductor and for a d-wave orthorhombic superconductor with a small s-wave component to its gap only the s-component contributes. It has been further argued that the effect of twins, in YBa₂ Cu₃ O_7-δ (YBCO) would lead to cancellation between pairs of twins, and so the observation of a current in c-axis YBCO-Pb experiments is evidence against a d-wave-type order parameter. We argue that there is evidence that the two twin orientations are not necessarily equally abundant in call cases.