Fermionized parafermions and symmetry-enriched Majorana modes

Understand

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.