Probing nonlocality of Majorana fermions in Josephson junctions of Kitaev chains connected to normal metal leads

Abstract

Kitaev chain (KC) is a prototypical model for the study of Majorana fermions (MFs). In the topological phase, a KC hosts two MFs at its ends. Being separated in space, these two MFs are nonlocal. The nonlocal transport in a KC biased between two normal metal leads is mediated by electron tunneling (ET) and crossed Andreev reflection (CAR). ET contributes positively while CAR contributes negatively to the nonlocal conductance. Enhanced CAR and hence a negative nonlocal conductance is a hallmark of nonlocality of MFs. But simple conductance measurements in the above setup cannot probe the nonlocality of MFs due to the almost cancellation of currents from ET and CAR. On the other hand, a Josephson junction between two KCs hosts two Andreev bound states (ABSs) at the junction formed by a recombination of Majorana fermions of the individual KCs. The energies of the ABSs are away from zero and can be changed by altering the superconducting phase difference. A Josephson junction between two finitely long KCs hosts two MFs at the two ends and two ABSs at the junction. We show that when normal metal leads are connected to two ends of such a Josephson junction, the nonlocal conductance of the setup can be negative for bias values equal to the energies of the ABSs. Thus the nonlocal conductance in such setup can probe the nonlocality of the constituent MFs.