Nonlocality of local Andreev reflection as a signature of topological superconductivity

We propose a method of distinguishing trivial and topological phases in Majorana wires by exploiting a peculiar nonlocality of the Majorana-mediated local Andreev reflection (LAR). To this end, we calculate the conductance and the local density of states (LDOS) in a three-terminal device. By combining the scattering matrix formalism and the Green's function approach, we show that in the trivial phase the local conductances are not affected by the decrease in the coupling to the normal lead at the opposite end of the wire. In the topological phase, however, LAR is suppressed by this lead-asymmetry. We explain this by showing that a zero-energy dip in the LDOS develops as the asymmetry in the couplings to the left and right normal leads increases. In addition, the local conductances show the exact same dependence on the lead-asymmetry in the presence of Majorana zero modes (MZMs), in stark contrast to trivial subgap states arising from inhomogeneities in the wire. Furthermore, by exploiting the control over the LDOS afforded by the lead-asymmetry, we propose a Majorana-based transistor in a Majorana wire-quantum dot setup [1]. Our work shows a distinctive signature of the Majorana nonlocality in terms of nonlocal effects on LAR, thus providing an additional diagnostic tool for a conclusive observation of MZMs.