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

Abhiram Soori

Published 2019-09-09Version 1

Kitaev chain is a prototypical model for the study of Majorana fermions~(MFs). In the topological phase, a Kitaev chain hosts two MFs at its ends. Being separated in space, these two MFs are nonlocal. When the Kitaev chain is connected to two normal metal leads, the nonlocal transport 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 definite signature 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 Kitaev chains hosts two Andreev bound states~(ABSs) at the junction formed by a recombination of Majorana fermions of the individual Kitaev chains. 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 Kitaev chains 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 and thus the nonlocal conductance of this setup can be used as a probe of the nonlocality of the constituent MFs.