A simple electronic ladder model harboring ${\mathbb{Z}}_4$ parafermions

Abstract

Parafermions are anyons with the potential for realizing non-local qubits that are resilient to local perturbations. Compared to Majorana zero modes, braiding of parafermions implements an extended set of topologically protected quantum gates. This, however, comes at the price that parafermionic zero modes can not be realized in the absence of strong interactions whose theoretical description is challenging. In the present work, we construct a simple lattice model for interacting spinful electrons with parafermionic zero energy modes. The explicit microscopic nature of the considered model highlights new realization avenues for these exotic excitations in recently fabricated quantum dot arrays. By density matrix renormalization group calculations, we identify a broad range of parameters, with well-localized zero modes, whose parafermionic nature is substantiated by their unique $8\pi$ periodic Josephson spectrum.

References in corpus (20)

• Non-Abelian Anyons and Topological Quantum Computation
• The ITensor Software Library for Tensor Network Calculations
• A four-qubit germanium quantum processor
• Exotic non-Abelian anyons from conventional fractional quantum Hall states
• Realization of a minimal Kitaev chain in coupled quantum dots
• Fractionalizing Majorana fermions: non-abelian statistics on the edges of abelian quantum Hall states
• Topological orbital ladders
• Time-Reversal-Invariant $Z_4$ Fractional Josephson Effect
• Tunable superconducting coupling of quantum dots via Andreev bound states in semiconductor-superconductor nanowires
• Non-Abelian parafermions in time-reversal invariant interacting helical systems
• Error estimates for extrapolations with matrix-product states
• Crossed Andreev reflection and elastic co-tunneling in a three-site Kitaev chain nanowire device
• Parity anomaly and spin transmutation in quantum spin Hall Josephson junctions
• ${\mathbb{Z}}_4$ Parafermions in an interacting quantum spin Hall Josephson junction coupled to an impurity spin
• Designing magnetic properties in CrSBr through hydrostatic pressure and ligand substitution
• Exciton transport in a germanium quantum dot ladder
• Coupled wire construction of a topological phase with chiral tricritical Ising edge modes
• Dynamical topological excitations in parafermion chains
• Quantum dots as parafermion detectors
• Two-channel Kondo problem in coupled interacting helical liquids

Cited by in corpus (1)

• Noninteracting tight-binding models for Fock parafermions