Effect of disorder in non-uniform hybrid nanowires with Majorana and fermionic bound states

TL;DR

This paper investigates how disorder affects Majorana and fermionic bound states in non-uniform hybrid nanowires, revealing new bound states and phase behaviors critical for quantum device applications.

Contribution

It introduces the effects of various disorder sources on topological phases and explores the formation and manipulation of fermionic bound states at topological π junctions in hybrid nanowires.

Findings

Disorder impacts the stability of topological phases in nanowires.

Fermionic bound states can localize at π junctions and mediate interactions between Majorana states.

The phase shift in Andreev spectra is influenced by junction properties.

Abstract

Majorana fermions in some model semiconductor nanowires proximity coupled with \emph{s}-wave superconductor have been investigated, as well as other intragap bound states in topological phase of a Rashba nanowire with non-uniform spin-orbit interaction (SOI). Various sources of disorder, such as disorder in semiconductor nanowire, bulk superconductor and semiconductor-superconductor interface, are included to characterize their effects on the stability of the topological phase. In the case of multiband semiconducting nanowires, the phase diagram of the system as a function of the chemical potential and magnetic field have been calculated. In two-band wire or two coupled single band wire, the phase of one band can be controlled through the other band, and these properties is critical to build multiband quantum device. When the SOI vector or magnetic field in semiconductor nanowire rapidly rotates by the angle $\pi $, changes its sign, a topological $\pi $ junction forms at the junction between two wire sections characterized by different directions of the SOI vectors or magnetic field. In this case, some fermionic bound states (FBS) can emerge inside the proximity gap, which localize at the topological $\pi $ junction, and coexist with Majorana bound states localized at the nanowire ends. Changing the position of the topological $\pi $ junction from one end to the other, the zero-energy FBS moves and can be used as mediator to transfer quantum information between two distance MFs. Meanwhile, the Andreev spectrum of the junction is qualitatively phase shift by $\pi $ compared to usual Majorana weak links. The FBS can act as quasiparticle traps and serve as an effective mediator of hybridization between two distant Majorana bound states (MBSs).