Degenerate Ground State in a MesoscopicYBa2Cu3O7−xGrain Boundary Josephson Junction

We have measured the current-phase relationship $I\left(\varphi \right)$ of symmetric 45° ${\mathrm{YBa}}_2{\mathrm{Cu}}_3{\mathrm{O}}_{7-x}$ grain boundary Josephson junctions. Substantial deviations of the Josephson current from conventional tunnel-junction behavior have been observed: (i) The critical current exhibits, as a function of temperature $T$, a local minimum at a temperature $T^{*}$. (ii) At $T\approx T^{*}$, the first harmonic of $I\left(\varphi \right)$ changes sign. (iii) For $T<\mathrm{}{T}^{*}$, the second harmonic of $I\left(\varphi \right)$ is comparable to the first harmonic, and (iv) the ground state of the junction becomes degenerate. The results are in good agreement with a microscopic model of Josephson junctions between $d$-wave superconductors.