Figure 1

Sketch of the grain boundary structure with different interface orientations (a). Reported planes are $a\mathrm{\text{−}}b$ planes on the (001) oriented side, and $a^{\prime }\mathrm{\text{−}}{b}^{\prime }$ planes on the (103) oriented side. The three interface orientations where a minimum of $J_C$ is expected ($AB$: $\theta =90°$; $BC$: $\theta =35°$; $CD$: $\theta =0°$) from purely geometrical considerations are also shown. (b) A side view of the (103) planes is illustrated to address in detail the case of the $\overline{BC}$ interface. $\overline{BC}$ is obtained as the normal to the vector $\overline{O{O}^{\prime }}$. $\overline{O{O}^{\prime }}$ is constructed in such a way that the projection $\overline{P{O}^{\prime }}$ on the $a^{\prime }\mathrm{\text{−}}{b}^{\prime }$ plane points towards a node of the order parameter in the (103) oriented side. The picture shows that for the angle $\theta =O^{\prime }\widehat{O}D=B\widehat{C}D$ the following relation applies: $\theta =O^{\prime }\widehat{O}D=\arctan [1/\sqrt{(}2)]\simeq 35°$.Reuse & Permissions

Figure 2

Current vs voltage ($I\mathrm{\text{−}}V$) characteristics of the junctions with $\theta =11°$ and $\theta =67°$ at $T=4.2\mathrm{K}$, respectively.Reuse & Permissions

Figure 3

Critical current density $J_C$ vs angle $\theta$ for two sets of junctions prepared on the same chip, $10\mu \mathrm{m}$ (triangles) and $4\mu \mathrm{m}$ (stars) wide, respectively ($T=4.2\mathrm{K}$). Solid lines connecting triangles and stars are guides for the eye. $J_C$ values are normalized to their maximum ($J_C\approx 7\times {10}^3\mathrm{A}/\mathrm{c}{\mathrm{m}}^{\mathrm{2}}$ for the $10\mu \mathrm{m}$ wide junctions). Experimental data are compared with the Sigrist-Rice theory applied to the usual $d$-wave OP symmetry (dashed line) and to a slightly different wave function with narrow lobes (dotted line), as shown in the inset.Reuse & Permissions

Figure 4

(a) Dependence of the critical current on the externally applied magnetic field H for $\theta =0°$ at $T=4.2\mathrm{K}$. (b) Scanning SQUID microscopy image of a $200\times 200\mu {\mathrm{m}}^{\mathrm{2}}$ area, enclosing tilt-tilt and twist-tilt GBs. The GBs are marked by the presence of spontaneous currents. The image was taken at $T=4.2\mathrm{K}$ in a nominally zero field cooling field.Reuse & Permissions