Transition from Fractional to Majorana Fermions in Rashba Nanowires

TLDR

The study investigates hybrid superconducting‑semiconducting nanowires with Rashba spin‑orbit interaction and helical magnetic fields. The authors analytically solve for Majorana and fractional‑fermion bound states and numerically map the phase diagram using Wronskian null‑space methods. The analysis reveals competing topological gaps that close and reopen, producing reentrance behavior, new Jackiw‑Rebbi fractional‑fermion phases that evolve into Majorana modes when superconductivity is added, and interaction‑enhanced Zeeman gaps.

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.