Abstract：We investigate the dc Josephson effect in one-dimensional junctions where a ring conductor is sandwiched between two semiconductor nanowires with proximity-induced superconductivity. Peculiar features of the Josephson effect arise due to the interplay of spin-orbit interaction and external Zeeman field. By tuning the Zeeman field orientation, the device can vary from 0 to $\pi$ junction. More importantly, nonzero Josephson current is possible at zero phase difference across the junction. Although this anomalous Josephson current is not relevant to the topological phase transition, its magnitude can be significantly enhanced when the nanowires become topological superconductors where Majorana bound states emerge. Distinct modulation patterns are obtained for the semiconductor nanowires in the topologically trivial and non-trivial phases. These results are useful to probe the topological phase transition in semiconductor nanowire junctions via the dc Josephson effect.
2016, Vol. 33 
