Fractional Fermions with Non-Abelian Statistics

Abstract

We introduce a novel class of low-dimensional topological tight-binding models that allow for bound states that are fractionally charged fermions and exhibit non-Abelian braiding statistics. The proposed model consists of a double (single) ladder of spinless (spinful) fermions in the presence of magnetic fields. We study the system analytically in the continuum limit as well as numerically in the tight-binding representation. We find a topological phase transition with a topological gap that closes and reopens as a function of system parameters and chemical potential. The topological phase is of the type BDI and carries two degenerate mid-gap bound states that are localized at opposite ends of the ladders. We show numerically that these bound states are robust against a wide class of perturbations.

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Cited by in corpus (10)

• Kramers Pairs of Majorana Fermions and Parafermions in Fractional Topological Insulators
• Fermionic and Majorana Bound States in Hybrid Nanowires with Non-Uniform Spin-Orbit Interaction
• Quantum Spin Hall Effect in Strip of Stripes Model
• Poor man's topological quantum gate based on the Su-Schrieffer-Heeger model
• Helical nuclear spin order in a strip of stripes in the Quantum Hall regime
• Topological phases, topological flat bands, and topological excitations in a one-dimensional dimerized lattice with spin-orbit coupling
• Quantum charge pumping through fractional Fermions in charge density modulated quantum wires and Rashba nanowires
• Topological gap states of semiconducting armchair graphene ribbons
• Detecting non-Abelian statistics of topological states on a chain of superconducting circuits
• Jackiw-Rebbi-type bound state carrying fractional fermion parity