Effects of electron scattering on the topological properties of nanowires: Majorana fermions from disorder and superlattices

TL;DR

This paper investigates how electron scattering, both regular and irregular, affects the topological states in superconducting nanowires, revealing that disorder can either destroy or induce topological order depending on the system.

Contribution

It demonstrates that disorder has contrasting effects on topological states in p-wave and Rashba wires, and shows how superlattice potentials can enhance topological phase space.

Findings

Disorder destroys topological order in p-wave wires beyond a critical strength.

Disorder can induce topological order in Rashba wires, reducing the need for clean samples.

Superlattice potentials can increase the phase space of topological states in disordered Rashba wires.

Abstract

We focus on inducing topological state from regular, or irregular scattering in (i) p-wave superconducting wires and (ii) Rashba wires proximity coupled to an s-wave superconductor. We find that contrary to common expectations the topological properties of both systems are fundamentally different: In p-wave wires, disorder generally has a detrimental effect on the topological order and the topological state is destroyed beyond a critical disorder strength. In contrast, in Rashba wires, which are relevant for recent experiments, disorder can {\it induce} topological order, reducing the need for quasiballistic samples to obtain Majorana fermions. Moreover, we find that the total phase space area of the topological state is conserved for long disordered Rashba wires, and can even be increased in an appropriately engineered superlattice potential.