Fermionized parafermions and symmetry-enriched Majorana modes

TL;DR

This paper introduces exact mappings from parafermion chains to one-dimensional fermionic systems, revealing novel symmetry-enriched Majorana modes with unique braiding and fusion properties, and proposes experimental protocols for their detection.

Contribution

It provides a new theoretical framework connecting parafermions to fermionic systems, enabling exploration of exotic Majorana-like modes with enriched symmetries.

Findings

Parafermion zero modes map to symmetry-enriched Majorana modes.

Fusion properties can be probed via anomalous pumping cycles.

A minimal protocol involves cycling a wire to produce edge magnetization with quadrupled periodicity.

Abstract

Parafermion zero modes are generalizations of Majorana modes that underlie comparatively rich non-Abelian-anyon properties. We introduce exact mappings that connect parafermion chains, which can emerge in two-dimensional fractionalized media, to strictly one-dimensional fermionic systems. In particular, we show that parafermion zero modes in the former setting translate into 'symmetry-enriched Majorana modes' that intertwine with a bulk order parameter---yielding braiding and fusion properties that are impossible in standard Majorana platforms. Fusion characteristics of symmetry-enriched Majorana modes are directly inherited from the associated parafermion setup and can be probed via two kinds of anomalous pumping cycles that we construct. Most notably, our mappings relate $\mathbb{Z}_4$ parafermions to conventional electrons with time-reversal symmetry. In this case, one of our pumping protocols entails fairly minimal experimental requirements: Cycling a weakly correlated wire between a trivial phase and time-reversal-invariant topological superconducting state produces an edge magnetization with quadrupled periodicity. Our work highlights new avenues for exploring 'beyond-Majorana' physics in experimentally relevant one-dimensional electronic platforms.