Mutation of Andreev into Majorana bound states in long superconductor-normal and superconductor-normal-superconductor junctions

We study one-dimensional topological superconductor-normal (SN) and superconductor-normal-superconductor (SNS) long junctions obtained by placing a topological insulating nanowire in the proximity of either one or two superconductor (SC) finite-size leads. Using the Majorana polarization (MP) order parameter introduced by Sticlet et al. [Phys. Rev. Lett. 108, 096802 (2012)], 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 a 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.