Critical-current diffraction patterns of grain-boundary Josephson weak links

We discuss the diffraction patterns and other characteristics of the critical current as a function of magnetic field in grain-boundary Josephson barriers. Diffraction patterns occur not just for SIS junctions but for all types of Josephson links, including SNS junctions, which may be present at grain boundaries in high-${\mathit{T}}_{\mathit{c}}$ superconductors. We discuss the generality of the Airy diffraction pattern, which is expected to characterize grain-boundary barriers in bulk material more accurately than the Fraunhofer pattern. The transport critical-current density in many bulk, granular high-${\mathit{T}}_{\mathit{c}}$ superconductors has a power-law dependence on very low magnetic fields, characteristic of averaged diffraction patterns, and cannot be fitted by an exponential magnetic-field dependence, which may result from the material properties of the barriers.