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In this study, we explore the Josephson current-phase relation within a planar diffuse tunneling superconducting multilayer junction subjected to a parallel magnetic field. Our investigation involves computing the supercurrent associated with a fixed jump in the phase of the order parameter at each of the two insulating interfaces, allowing us to derive the current-phase relation for the junction. Employing perturbation theory in junction conductance, we determine both the first and second harmonics of the current-phase relation under specific magnetic field conditions. Notably, the presence of a strong spin-orbit interaction in the middle region of the junction introduces an anomalous Josephson effect. The interplay between spin-orbit and Zeeman interactions results in the emergence of an effective vector potential. This specific characteristic induces a phase shift in each harmonic of the current-phase relation without altering the overall shape of the relation. The mechanism for the Josephson diode effect is discussed for disordered junctions of multiband superconductors.
Osin et al. (2024) studied this question.