Magnetic-field dependence of the critical current of Abrikosov - Josephson junction in superconducting film

Low-angle boundaries between single-crystal domains (with misorientation angles theta similar to 1 degrees) in epitaxial films of high-temperature superconductors are crucial for achievement of high values of critical current and low microwave losses. Such boundaries with high transparency for superconducting current (as compared with usual Josephson junctions) for temperatures T rather close to the critical one T(c) possess properties of Abrikosov - Josephson (A-J) junctions, as well as boundaries with theta similar to 5 degrees-10 degrees in films on bi-crystal substrates for the whole temperature range. Magnetic flux penetrates into such junctions by the means of A-J vortices, which differ from the Abrikosov ones by the presence of phase cores rather then normal-metallic cores, and from the Josephson ones by non-local dependence between the phase difference and magnetic field. Generalization of the well-known Fraunhofer-like magnetic-field dependence of the Josephson critical current is presented for the case of A-J junction in the field normal to the film plane.