Novel 0-pi transitions in Josephson junctions between noncentrosymmetric superconductors

We study the Josephson effect between two noncentrosymmetric superconductors (NCSs) with opposite polarization vectors of Rashba spin-orbit coupling (RSOC). We find a 0-pi transition driven by the triplet-singlet ratio of NCSs. Different from conventional 0-pi transitions, the Andreev bound states change their energy range instead of phase shift in the 0-pi transition found here. This novel property results in a feature that the critical current becomes almost zero at the transition point, not only a minimum. Furthermore, when the directions of RSOC polarization vectors are the same in two NCSs, the similar effect can also be found in the presence of a perpendicular exchange field or a Dresselhause spin-orbit coupling in the interlayer. We find novel oscillations of critical current without 0-pi transition. These novel 0-pi transitions or oscillations of critical current present new understanding of the Josephson effect and can also serve as a tool to determine the unknown triplet-singlet ratio of NCSs.