Anomalous Josephson effect between d-wave superconductors through a two-dimensional electron gas with both Rashba spin–orbit coupling and Zeeman splitting

Based on the Bogoliubov–de Gennes equation and the extended McMillan’s Green’s function formalism, we study theoretically the Josephson effect between two d-wave superconductors bridged by a ballistic two-dimensional electron gas with both Rashba spin–orbit coupling and Zeeman splitting. We show that due to the interplay of Rashba spin–orbit coupling and Zeeman splitting and d-wave pairing, the current–phase relation in such a heterostructure may exhibit a series of novel features and can change significantly as some relevant parameters are tuned. In particular, anomalous Josephson current may occur at zero phase bias under various different situations if both time reversal symmetry and inversion symmetry of the system are simultaneously broken, which can be realized by tuning some relevant parameters of the system, including the relative orientations and the strengths of the Zeeman field and the spin–orbit field in the bridge region, the relative orientations of the a axes in two superconductor leads, or the relative orientations between the Zeeman field in the bridge region and the a axes in the superconductor leads. We show that both the magnitude and the direction of the anomalous Josephson current may depend sensitively on these relevant parameters.