Josephson current through a quantum dot coupled to a Majorana zero mode.

Employing the Green's function method, we investigate the Josephson current through a quantum dot side coupled to a topological superconducting nanowire sustaining a pair of Majorana zero modes. It is found that the Josephson current is blocked when the quantum dot is side coupled to a superconducting nanowire in a topologically trivial phase. However, when the topological superconducting nanowire transitions from a topologically trivial to a topologically non-trivial phase, an Andreev bound state arises at the zero Fermi energy of the quantum dot due to leakage of the Majorana zero mode. Thus a Josephson current can be induced by leakage of the Majorana zero mode into the quantum dot. The Josephson current shows a plateau-like structure and a clear-cut trivial/non-trivial phase transition, as a function of a Zeeman field imposed on the system. The transition and plateau-like structure can be used to probe the existence of the Majorana zero mode. The current-phase relation has also been studied.