Supercurrent reversal in Zeeman-split Josephson junctions

We study theoretically the shape of the current-phase relation in a Josephson junction comprising the Zeeman-split superconductors (ZSs) and a normal metal (N). We show that at low temperatures the Josephson current in the ZS/N/ZS junctions exhibits an additional reversal in direction at a certain phase difference ${\phi }_c\in (0,\pi )$. Calculating the spectral Josephson current, the band-splitting due to the Zeeman interaction is shown to cause the level crossing in the spectra of the Andreev bound states and the sign reversal in the Josephson current. Additionally, we propose an alternative method to electrically control the critical phase difference ${\phi }_c$ by tuning the Rashba spin-orbit coupling, eliminating the need for manipulating magnetizations.