$\mathit{c}$-axis Josephson Tunneling between ${\mathrm{YBa}}_2{\mathrm{Cu}}_3{O}_{7-\delta }$ and Pb: Direct Evidence for Mixed Order Parameter Symmetry in a High- $T_c$ Superconductor

We report a new class of $c$-axis Josephson tunneling experiments in which a conventional superconductor (Pb) is deposited across a single twin boundary of a $\mathrm{YBa}{}_2{\mathrm{Cu}}_3{\mathrm{O}}_{7-\delta }$ (YBCO) crystal. We measure the critical current as a function of the magnitude and angle of a magnetic field applied in the plane of the junction. In all samples, we observe a clear experimental signature of an order parameter phase shift across the twin boundary. These results provide strong evidence for mixed $d$- and $s$-wave pairing in YBCO, with a reversal in the sign of the $s$-wave component across the twin boundary.