We study the Josephson current (supercurrent) in a system consisting of two superconductors connected to a single-level quantum dot (QD), which is also side-coupled to a nanowire hosting Majorana bound states (MBSs). Our results show that the MBSs change both the peak height and position in the current-carrying density of states (CCDOS), and this determines the amplitude of the Josephson current due to the phase difference between the superconductors. By adjusting the energy level in the QD and MBSs-QD hybridization strengths, the magnetic flux penetrating through the closed circuit formed by the QD and the nanowire as well as the direct overlap between the MBSs, one can fully control the electron transport processes. The present results are useful in superconductor-based electrical devices and the newly developed area of superconducting coated conductors.

We investigate the behavior of the Josephson current in a system composed of a quantum dot (QD) sandwiched between two nanowires by using the nonequilibrium Green’s function technique. We consider that the nanowires are in proximity to s-wave superconducror substrates, and Majorana bound states (MBSs) are induced at their ends. It is also assumed that the two nanowires are not aligned in the same orientation, but form a bent angle with respect to each other. It is found that when only one spin state on the QD is coupled to the left nanowire, the Josephson current is the typical sinusoidal function of the phase difference between the two nanowires. If both spin states hybridize to the MBSs with equal coupling strengths, the Josephson current then is not a sinusoidal function of the phase difference. In particular, when the bent angle between the two nanowires is π/2 and the two modes of the MBSs in each nanowire are decoupled from each other, the Josephson current is enhanced by about twenty times in magnitude as compared to the former case. Moreover, the simultaneously enhanced currents of the two spin directions are of the same magnitude but flow in opposite directions and they induce a large pure spin current. Our results also show that this abnormally enhanced Josephson current will be suppressed by a vertical magnetic field applied to the QD.