Josephson Diode Effect in <i>d</i>-Wave Superconductor/Ferromagnet/<i>d</i>-Wave Superconductor Junction with Interfacial Rashba Spin–Orbit Coupling

Abstract We provide a theoretical study of the effect of interfacial Rashba spin–orbit coupling (SOC) and insulating interfaces on the Josephson effect between two $d$-wave superconducting electrodes connected through a ferromagnet, based on the Bogoliubov–de Gennes approach and the extended McMillan’s Green’s function formalism. Our results reveal that the appearance of the anomalous and diode Josephson effects is conditioned by the presence of interfacial Rashba SOC, a nonzero component of exchange field perpendicular to the plane of the junction, and the nonsymmetric orientation of two $d$-wave superconducting electrodes, which is in accordance with the presented symmetry analysis. We show that enhancement of nonreciprocity (higher than 30%) of the supercurrent in this kind of junction can be realized by tuning the orientation of both superconductors, the strength of the exchange field in the ferromagnetic barrier, and Rashba SOC at the interfaces, as well as optimizing the interface transparency. We predict that phase transition between 0-like and $\pi$-like states, which can occur through phase jump or be continuous, can be achieved not only by changing the strength of the exchange field, but also by modulating the strength of the Rashba SOC. Our results also show the significant temperature dependence of diode characteristics and predict the possibility of a temperature-induced 0–$\pi$-like phase transition.