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Multiple Andreev reflections in s-wave superconductor-quantum dot- topological superconductor tunnel junctions and Majorana bound states

We calculate the current as a function of applied voltage in non-topological s-wave superconductor-quantum dot-topological superconductor tunnel junction. We consider the type of TS which hosts two Majorana bound states (MBS) at the ends of a semiconductor quantum wire or of a chain of magnetic atoms in the proximity with s-wave superconductor. We find that the $I-V$ characteristic of such system in the regime of big voltages has a typical two dot shape and is ornamented by peaks of multiple Andreev reflections. We also consider the other options when the zero energy states are created by disorder (here by Shiba states) or by Andreev zero energy bound states at the surface of quantum dot and superconductor. The later are obtained by tuning the magnetic field to a specific value. Unlike the last two cases the MBS $I-V$ curves are robust to change the magnetic field. Therefore, the magnetic field dependence of the tunneling current can serve as a unique signature for the presence of a MBS.