Anomalous Josephson effect in a planar hybrid structure with the spin–orbit coupling

The way of formation of controlled phase inhomogeneity in a hybrid structure consisting of a short Josephson junction between two superconducting thin films, with one electrode partially coated with a ferromagnetic insulator, has been theoretically studied. The joint action of spin splitting and the Rashba spin–orbit coupling at the superconductor–ferromagnet interface leads to the generation of a spontaneous supercurrent, which changes the transport properties of the junction. The critical current and the current–phase relation of this hybrid structure have been calculated; it has been shown that this structure can be used to form an anomalous $\varphi_0$ Josephson junction with the phase shift $\varphi_0$ smoothly varying over a wide range.