We investigate theoretically the Josephson junction of semiconductor nanowire with strong spin-orbit (SO) interaction in the presence of magnetic field. By using a tight-binding model, the energy levels En of Andreev bound states are numerically calculated as a function of phase difference φ between two superconductors in the case of short junctions. The DC Josephson current is evaluated from the Andreev levels. In the absence of SO interaction, a 0-π transition due to the magnetic field is clearly observed. In the presence of SO interaction, the coexistence of SO interaction and Zeeman effect results in En(−φ)=En(φ), where the anomalous Josephson current flows even at φ=0. In addition, the direction-dependence of critical current is observed, in accordance with experimental results.
@article{arxiv.1402.0305,
title = {Anomalous Josephson effect induced by spin-orbit interaction and Zeeman effect in semiconductor nanowires},
author = {Tomohiro Yokoyama and Mikio Eto and Yuli V. Nazarov},
journal= {arXiv preprint arXiv:1402.0305},
year = {2014}
}