Josephson diode effect in one-dimensional quantum wires connected to superconductors with mixed singlet-triplet pairing

The Josephson diode effect (JDE), characterized by asymmetric critical currents in a Josephson junction, has drawn considerable attention in the field of condensed matter physics. We investigate the conditions under which JDE can manifest in a one-dimensional Josephson junction composed of a spin-orbit-coupled quantum wire with an applied Zeeman field, connected between two superconductors. Our study reveals that while spin-orbit coupling (SOC) and a Zeeman field in the quantum wire are not sufficient to induce JDE when the superconductors are purely singlet, introduction of triplet pairing in the superconductors leads to the emergence of JDE. This finding highlights the potential of JDE as a probe for triplet superconductivity. We further demonstrate that even in absence of SOC in the quantum wire, JDE can arise when the directions of the triplet pairing and the Zeeman field are non-collinear, provided the superconductors exhibit mixed singlet-triplet pairing. Additionally, we identify specific conditions under which JDE is absent, namely, when the pairing is purely triplet and the directions of the SOC and the triplet pairing are perpendicular. Our findings indicate that JDE is always accompanied by anomalous Josephson effect. The diode effect coefficient is found to oscillate with variations in the chemical potential of the quantum wire, driven by Fabry-P\'erot interference effects. Our results suggest that quantum wires connected across superconductors can serve as effective platforms for probing triplet superconductivity through the observation of JDE.