Fano-Josephson effect in the junction with DIII-class topological and s-wave superconductors

We investigate the Josephson effects in the junction formed by the direct and indirect couplings between DIII-class topological and s-wave superconductors. As a result, the Josephson current is found to oscillate in period 2π. The presence of Majorana doublet in the DIII-class superconductor renders the current finite at the case of zero phase difference, with its sign determined by the fermion parity of such a junction. In addition to the dot level and intradot Coulomb interaction, the Fano interference is an important factor to adjust the Josephson current. It is believed that these results will be helpful in understanding the transport properties of the DIII-class superconductor.