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For a tight-binding model with nearest-neighbor attraction and a small orthorhombic distortion, we find a phase diagram for the gap at zero temperature which includes three distinct regions as a function of filling. In the first, the gap is a mixture of mainly d-wave with a smaller extended s-wave part. This is followed by a region in which there is a rapid and continuous increase in the s-wave part accompanied by a rapid increase in relative phase between s and d from 0 to~. Finally, there is a region of dominant s with a mixture of d and zero phase. In the mixed region with a finite phase, the s-wave part of the gap can show a sudden increase with decreasing temperature accompanied with a rapid increase in phase with an attendant change in superconducting properties.

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There should be no Josephson current between a CuO» plane with a gap of d» symmetry and a x conventional s-wave superconductor. Nevertheless such a current is observed to exist between YBa»Cu307 (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 d» symmetry but with a minor extended s-wave comxy ponent. The resultant Josephson current for YBCO-Pb junctions is in good agreement with experiment. I. INTRGDUCTIQN Many experiments' which probe the temperature dependencies and other properties of the superconducting state without and with impurities ' have been interpreted as evidence that the gap in the Cu02 planes of the high-T, oxides exhibits d»» symmetry. Many of these observations, however, could equally well be interpreted as due to an extended s-wave gap with zeros on the Fermi surface. Two recent experiments, designed very specifically to measure the phase of the gap, have led to contradictory results, one favoring d-wave the other swave. ' While there are many theoretical arguments in favor of d wave, '' counter arguments have also been put forward.In a very recent experiment, Sun et al. have observed a Josephson current between YBCO and Pb for a tunnel junctio~with current Aowing perpendicular to the planes.The authors point out that this is unexpected if the YBCO is a pure d-wave superconductor. Because of the existence of chains in YBCQ the a and b directions are not equivalent and, in fact, YBCO exhibits a large anisotropy in value of zero-temperature penetration depth which would not be the case for pure tetragonal symmetry. This has been interpreted as suggesting that a substantial portion of the superconducting condensate resides in the chains in this material. Further, localdensity-approximation band-structure calculations have found a complicated Fermi surface with a fairly planar part identified with the chains, in addition to the usual CuQ2 part of the Fermi surface. Several bands should be accounted for in any complete discussion of the superconducting properties of this compound. While a multiband model may be necessary for a detailed discussion, it is very complicated and would introduce many additional parameters in the resulting discussion. In this paper we account for a-b anisotropy only through a very simplified model, namely, an anisotropic effective mass approxima-tion within a single CuO2 plane. While this is not fully realistic, the model has the virtue of simplicity and introduces into the calculation only a single additional parameter, namely the electron mass anisotropy, which can, in fact, be At to the measured penetration depth anisotropy. To describe the superconducting condensation we employ the model of Millis, ...

For a two-layer system in a weak-coupling BCS formalism any interlayer interaction, regardless of its sign, enhances the critical temperature. The sign has an effect upon the relative phase of the order parameter in each of the two planes but not upon its magnitude. When one of the planes has a dispersion consistent with CuO chains and no intrinsic pairing interaction there is both an enhancement of the critical temperature and an sϩd mixing in both layers as the interlayer interaction is increased. The magnetic penetration depth, c-axis Josephson tunneling, density of states, and Knight shift are calculated for several sets of model parameters.