Electronic Tunnelling in Superconductor/Quantum-Dot Josephson Junction Side-Coupled to Majorana Nanowire

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.