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 a nontopological s-wave superconductor-quantum dot-topological superconductor (TS) tunnel junction. We consider the type of TS which hosts two Majorana bound states (MBSs) at the ends of a semiconductor quantum wire or of a chain of magnetic atoms in the proximity with an s-wave superconductor. We find that the I-V characteristic of such a 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 (hereby Shiba states) or by Andreev zero-energy bound states at the surface of a quantum dot and a 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.