Fermionic and Majorana Bound States in Hybrid Nanowires with Non-Uniform Spin-Orbit Interaction

TL;DR

This paper investigates bound states in Rashba nanowires with non-uniform spin-orbit interaction, revealing fermionic states inside the gap that coexist with Majorana states and could impact topological quantum computing.

Contribution

It provides analytical and numerical analysis of fermionic and Majorana bound states in nanowires with non-uniform SOI, highlighting the emergence and properties of FBS.

Findings

FBS can emerge inside the proximity gap at SOI junctions.

FBS energy depends on SOI angle and lengthscale of variation.

FBS can hybridize into double quantum dot-like states.

Abstract

We study intragap bound states in the topological phase of a Rashba nanowire in the presence of a magnetic field and with non-uniform spin orbit interaction (SOI) and proximity-induced superconductivity gap. We show that fermionic bound states (FBS) can emerge inside the proximity gap. They are localized at the junction between two wire sections characterized by different directions of the SOI vectors, and they coexist with Majorana bound states (MBS) localized at the nanowire ends. The energy of the FBS is determined by the angle between the SOI vectors and the lengthscale over which the SOI changes compared to the Fermi wavelength and the localization length. We also consider double-junctions and show that the two emerging FBSs can hybridize and form a double quantum dot-like structure inside the gap. We find explicit analytical solutions of the bound states and their energies for certain parameter regimes such as weak and strong SOI. The analytical results are confirmed and complemented by an independent numerical tight-binding model approach. Such FBS can act as quasiparticle traps and thus can have implications for topological quantum computing schemes based on braiding MBSs.