Josephson diode effect in a ballistic single-channel nanowire

When time-reversal and inversion symmetry are broken, superconducting circuits may exhibit a so-called diode effect, where the critical currents for opposite directions of the current flow differ. In recent years, this effect has been observed in a multitude of systems and the different physical ingredients that may yield such an effect are well understood. On a microscopic level, the interplay between spin-orbit coupling and a Zeeman field may give rise to a diode effect in a single Josephson junction. However, so far there is no analytical description of the effect within a simple model. Here we study a single channel nanowire with Rashba spin-orbit coupling and in the presence of a Zeeman field. We show that the different Fermi velocities and spin projections of the two pseudo-spin bands lead to a diode effect. Simple analytical expressions for the diode efficiency can be obtained in limiting cases.