Influence of the Rashba effect on the Josephson current through a superconductor/Luttinger liquid/superconductor tunnel junction

The Josephson current through a one-dimensional quantum wire with Rashba spin-orbit and electron-electron interactions is calculated. We show that the interplay of Rashba and Zeeman interactions gives rise to an anomalous phase shift in the current-phase relation for the supercurrent. The electron dispersion asymmetry induced by the Rashba interaction in a Luttinger-liquid wire plays a significant role when the electron-electron interaction is not strong and for poorly transmitting junctions. It is shown that for a weak or moderate electron-electron interaction the spectrum of plasmonic modes confined to the normal part of the junction becomes quasi-random in the presence of dispersion asymmetry. The resonance effects which are significant for transport properties of weakly interacting electrons in symmetric junctions survive in the presence of a strong Rashba interaction only for special boundary conditions at normal metal/superconductor interfaces