Transition from fractional to Majorana fermions in Rashba nanowires

TL;DR

This paper explores how Rashba nanowires transition from hosting fractional fermions to Majorana fermions, revealing complex phase behavior influenced by magnetic fields, superconductivity, and electron interactions.

Contribution

It provides analytical solutions and a phase diagram for the transition between fractional and Majorana fermions in Rashba nanowires, highlighting the role of magnetic fields and interactions.

Findings

Reentrant topological phases with two gap closures

Existence of fractional fermion bound states of Jackiw-Rebbi type

Magnetic fields alone can fully gap the system and induce FFs that become MFs with superconductivity

Abstract

We study hybrid superconducting-semiconducting nanowires in the presence of Rashba spin-orbit interaction as well as helical magnetic fields. We show that the interplay between them leads to a competition of phases with two topological gaps closing and reopening, resulting in unexpected reentrance behavior. Besides the topological phase with localized Majorana fermions (MFs) we find new phases characterized by fractionally charged fermion (FF) bound states of Jackiw-Rebbi type. The system can be fully gapped by the magnetic fields alone, giving rise to FFs that transmute into MFs upon turning on superconductivity. We find explicit analytical solutions for MF and FF bound states and determine the phase diagram numerically by determining the corresponding Wronskian null space. We show by renormalization group arguments that electron-electron interactions enhance the Zeeman gaps opened by the fields.