Properties of high-${\mathit{T}}_{\mathit{c}}$ Josephson junctions with ${\mathrm{Y}}_{0.7}$${\mathrm{Ca}}_{0.3}$${\mathrm{Ba}}_2$${\mathrm{Cu}}_3$${\mathrm{O}}_{7\mathrm{-}\mathrm{\delta }}$ barrier layers

We report the use of ${\mathrm{Y}}_{0.7}$ ${\mathrm{Ca}}_{0.3}$ ${\mathrm{Ba}}_2$ ${\mathrm{Cu}}_3$ ${\mathrm{O}}_{7\mathrm{-}\mathrm{\delta }}$ as an epitaxial barrier between ${\mathrm{YBa}}_2$ ${\mathrm{Cu}}_3$ ${\mathrm{O}}_{7\mathrm{-}\mathrm{\delta }}$ (YBCO) electrodes in high-${\mathit{T}}_{\mathit{c}}$ superconductor-normal-superconductor edge junctions. Ca-doped YBCO is an overdoped version of YBCO, and it has an excellent lattice and thermal expansion match with YBCO. We show that these junctions exhibit clean interfaces with resistances smaller than ${10}^{\mathrm{-}10}$ Ω ${\mathrm{cm}}^2$. We present the temperature dependence of the critical current density ${\mathit{J}}_{\mathit{c}}$ and the junction resistance ${\mathit{R}}_{\mathit{n}}$ for junctions with 200, 400, and 600 Å thick barriers of ${\mathrm{Y}}_{0.7}$ ${\mathrm{Ca}}_{0.3}$ ${\mathrm{Ba}}_2$ ${\mathrm{Cu}}_3$ ${\mathrm{O}}_{7\mathrm{-}\mathrm{\delta }}$. As the temperature decreases, the resistance of the junction decreases faster than the resistance calculated from the resistivity of a ${\mathrm{Y}}_{0.7}$ ${\mathrm{Ca}}_{0.3}$ ${\mathrm{Ba}}_2$ ${\mathrm{Cu}}_3$ ${\mathrm{O}}_{7\mathrm{-}\mathrm{\delta }}$ film. We analyze our data by considering various possibilities for the microstructure in the barrier region. We discuss the ideal conventional proximity effect, diffusion between the barriers and the electrodes, and doping fluctuations inside the barrier. We find that combinations of these ideas explain the observed behavior with reasonable parameters.