Mutation of Andreev into Majorana bound states in long NS and SNS junctions

TL;DR

This paper investigates how Andreev bound states in long topological nanowire junctions can evolve into Majorana bound states, which are detectable via tunneling spectroscopy, revealing new topological phenomena.

Contribution

It demonstrates the transformation of Andreev bound states into Majorana bound states in long NS and SNS junctions using the Majorana Polarization order parameter.

Findings

Extended Andreev bound states acquire finite Majorana polarization.

Zero-energy states in SN junctions carry a full Majorana fermion.

Phase difference of π in SNS junctions yields two Majorana fermions.

Abstract

We study one-dimensional topological SN and SNS long junctions obtained by placing a topological insulating nanowire in the proximity of either one or two SC finite-size leads. Using the Majorana Polarization order parameter (MP) introduced in Phys. Rev. Lett. 108, 096802 (2012)(arxiv:1109.5697) we find that the extended Andreev bound states (ABS) of the normal part of the wire acquire a finite MP: for a finite-size SN junction the ABS spectrum exhibits a zero-energy extended state which carries a full Majorana fermion, while the ABS of long SNS junctions with phase difference $\pi$ transform into two zero-energy states carrying two Majorana fermions with the same MP. Given their extended character inside the whole normal link, and not only close to an interface, these Majorana-Andreev states can be directly detected in tunneling spectroscopy experiments.