Abstract
We present an analysis of Josephson effects in one quantum-dot-embedded junction with one s-wave superconductor (SC) and two topological superconductors (TSs). It is found that when superconducting phase difference is applied between the two TSs, the dot-SC coupling can efficiently modulate the fractional Josephson effect, including the changes of the supercurrent oscillation direction and period. Even though the polarization directions of the TSs are opposite, the dot-SC coupling enables to drive the fractional Josephson effect between the TSs. Next, as the superconducting phase difference is introduced between the TSs and SC, only the normal Josephson effect takes place.
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