Fermionized Parafermions and Symmetry-Enriched Majorana Modes
Abstract: Majorana zero modes, particles that exhibit non-Abelian statistics, are theorized to exist in special one-dimensional wire geometries. These exotic particles have received much attention, both theoretical and experimental, due to their interesting physics and potential use for topological quantum computation. Parafermion zero modes are generalizations of Majorana modes that possess richer non-Abelian-anyon properties. Though these zero modes require two-dimensional hosts to exist, we introduce exact mappings that connect Z_4 parafermion chains to strictly one-dimensional fermionic systems with time-reversal symmetry. Parafermion zero modes 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. Our work highlights new avenues for exploring 'beyond-Majorana' physics in experimentally relevant one-dimensional electronic platforms, including proximitized ferromagnetic chains.