Influence of an interacting quantum dot on the fractional Josephson effect

We present the influence of an interacting quantum dot on the fractional Josephson effect in the junction constructed by two topological superconducting wires where Majorana zero modes exist. It is found that the intradot Coulomb interaction plays a nontrivial role in adjusting the magnitude and direction of the Josephson current. Moreover, despite the change of coupling manner between the two Majorana zero modes, appropriate Coulomb strengths are able to induce the occurrence of normal Josephson effect. With these results, the influence of one quantum dot on the fractional Josephson effect can be understood.