Interface roughness and proximity effect on a c-axis Josephson junction between s-wave and d-wave superconductors

The scanning superconducting quantum interference device microscope on tri-crystal high-temperature superconductor (HTSC) samples unambiguously identifies the d-wave pairing symmetry as a predominant component. This fact was also seen clearly from the current phase relation (CPR) for an in-plane junction between HTSC's, where both $\ensuremath{\pi}$ periodicity and $2\ensuremath{\pi}$ periodicity are observed, depending on the relative crystal orientation. However, for c-axis junctions between HTSC's and conventional superconductor, ac Josephson effect shows that the main Shapino steps occur at $V=nhf/2e$ $(n$ is integer) and thus a significant s-wave component is indicated. To understand the experimental measurements, we have studied interface roughness and proximity effect on CPR of such junctions. The order parameter profiles and current phase relation are computed self-consistently using the quasiclassical theory and rough interface model. Our results suggest that the existence of a minor surface s-wave component stemming from a repulsive s-channel pairing potential in the d-wave superconductor is able to give a coherent picture.