Non-sinusoidal current-phase relation controlled by spin-orbit coupling

We theoretically show the origin of the non-sinusoidal current phase relation (CPR). The Josephson current in the ZS/N/ZS junctions changes suddenly its direction at a certain phase difference (i.e., critical phase difference $\phi_c$), where ZS and N stand for the Zeeman-splitting superconductor and the normal metal. As a consequence, their CPRs become non-sinusoidal. Calculating the spectral Josephson current, the band-splitting by the Zeeman interaction plays an important role in reversing the current and determines $\phi_c$. We also propose a method to control non-sinusoidal CPR. The critical phase in the non-sinusoidal CPR can be controlled by tuning the Rashba spin-orbit interaction instead of by manipulating the magnetizations.