Andreev levels spectroscopy of topological three-terminal junctions

We calculate the differential conductance at a probe inserted in the weak link of a topological Josephson junction, consisting of a semiconducting nanowire deposited on top of two separated superconductors. Our aim is to understand how the peculiar features in the spectrum of Andreev bound states, arising due to the presence of Majorana bound states at the ends of the two topological superconducting wires defining the junction, can be determined through a measurement of the differential conductance. We find that when the probe allows a single propagating mode, the differential conductance presents a dip at zero voltage of zero conductance close to the position where the spectrum exhibits the topologically protected crossing. This can be viewed as a signature of the presence of Majorana states, which does not require fermion parity conservation and is robust against parameters' changes, as well as disorder. On the contrary, when the probe allows two or more propagating modes the differential conductance resembles the spectrum of Andreev bound states. This has been established making use of both numerical and analytical methods