From Andreev bound states to Majorana fermions in topological wires on superconducting substrates : a story of mutation

TL;DR

This paper investigates how the proximity effect influences the evolution of Andreev bound states into Majorana fermions in topological nanowires on superconducting substrates, highlighting the effects of tunnel coupling strength and disorder.

Contribution

It introduces a Green's function approach to study the transition from Andreev states to Majorana fermions and explores how strong coupling and disorder affect their stability.

Findings

Strong tunnel coupling can destroy Majorana states.

Disorder and quasiparticle broadening can induce topological phase transitions.

Inhomogeneous superconductors influence Majorana fermion formation.

Abstract

We study the proximity effect in a topological nanowire tunnel coupled to an s-wave superconducting substrate. We use a general Green's function approach that allows us to study the evolution of the Andreev bound states in the wire into Majorana fermions. We show that the strength of the tunnel coupling induces a topological transition in which the Majorana fermionic states can be destroyed when the coupling is very strong. Moreover, we provide a phenomenologial study of the effects of disorder in the superconductor on the formation of Majorana fermions. We note a non-trivial effect of a quasiparticle broadening term which can take the wire from a topological into a non-topological phase in certain ranges of parameters. Our results have also direct consequences for a nanowire coupled to an inhomogenous superconductor.