Majorana dc Josephson current mediated by a quantum dot

The Josephson supercurrent through a hybrid Majorana-quantum dot-Majorana junction is investigated. We particularly analyze the effect of spin-selective coupling between the Majorana and quantum dot states, which only emerges in the topological phase and will influence the current through bent junctions and/or in the presence of magnetic fields in the quantum dot. We find that the characteristic behavior of the supercurrent through this system is quite counterintuitive, differing remarkably from the resonant tunneling, e.g. through the similar (normal phase) superconductor-quantum dot-superconductor junction. Our analysis is carried out under the influence of the full set-up parameters and for both the 2 pi and 4 pi periodic currents. The present study is expected to be relevant to the future exploration of applications of Majorana-nanowire circuits.NBRP of China [2015CB921102]; NSF-China [11675016, 11274364, 11574007]; Beijing Natural Science Foundation [1164014]; China Postdoctoral Science Foundation [2016M591103]; Fundamental Research Funds for the Central UniversitiesSCI(E)ARTICLE192