Supercurrent reversal in Zeeman-split Josephson junctions

We theoretically study 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 a supercurrent reversal at a certain phase difference ${\ensuremath{\varphi}}_{c}\ensuremath{\in}(0,\ensuremath{\pi})$. By calculating the spectral Josephson current, we demonstrate that the band splitting due to the Zeeman interaction causes the level crossing in the spectra of the Andreev bound states and the sign reversal of the Josephson current. Additionally, we propose an alternative method to observe the supercurrent reversal. Tuning the Rashba spin-orbit coupling electrically, one can control the critical phase difference ${\ensuremath{\varphi}}_{c}$, eliminating the need for manipulating two magnetizations independently.