Tunability of Andreev levels via spin-orbit coupling in Zeeman-split Josephson junctions

We study Andreev reflection and Andreev levels $\ensuremath{\varepsilon}$ in Zeeman-split superconductor/Rashba wire/Zeeman split superconductor junctions by solving the Bogoliubov--de Gennes equation. We theoretically demonstrate that the Andreev levels $\ensuremath{\varepsilon}$ can be controlled by tuning either the strength of Rashba spin-orbit interaction or the relative direction of the Rashba spin-orbit interaction and the Zeeman field. In particular, it is found that the magnitude of the band splitting is tunable by the strength of the Rashba spin-orbit interaction and the length of the wire, which can be interpreted by a spin precession in the Rashba wire. We also find that if the Zeeman field in the superconductor has the component parallel to the direction of the junction, the $\ensuremath{\varepsilon}\ensuremath{-}\ensuremath{\phi}$ curve becomes asymmetric with respect to the superconducting phase difference $\ensuremath{\phi}$. Whereas the Andreev reflection processes associated with each pseudospin band are sensitive to the relative orientation of the spin-orbit field and the exchange field, the total electric conductance interestingly remains invariant.