Clock model and parafermions in Rashba nanowires

TL;DR

This paper explores how tuning parameters in Rashba nanowires with strong interactions can induce a gapless parafermion phase described by a self-dual sine-Gordon model, enabling localized zero-energy parafermion states.

Contribution

It introduces a novel mapping of the critical parafermion phase in Rashba nanowires to the $ ext{Z}_4$ parafermion clock model, and proposes a method to generate zero-energy parafermion bound states.

Findings

Identification of a gapless critical parafermion phase in Rashba nanowires.

Explicit mapping to the $ ext{Z}_4$ parafermion clock model.

Proposal to generate localized zero-energy parafermion states.

Abstract

We consider a semiconducting nanowire with Rashba spin-orbit interaction subjected to a magnetic field and in the presence of strong electron-electron interactions. When the ratio between Fermi and Rashba momenta is tuned to $1/2$, two competing resonant multi-particle scattering processes are present simultaneously and the interplay between them brings the system into a gapless critical parafermion phase. This critical phase is described by a self-dual sine-Gordon model, which we are able to map explicitly onto the low-energy sector of the $\mathbb{Z}_4$ parafermion clock chain model. Finally, we show that by alternating regions in which only one of these two processes is present one can generate localized zero-energy parafermion bound states.