$Z_4$ parafermion $\pm \pi /2$ modes in interacting periodically driven superconducting chain

Abstract

We theoretically report the emergence of $Z_4$ parafermion edge modes in a periodically driven spinful superconducting chain with modest fermionic Hubbard interaction. These parafermion edge modes represent $\pm \pi /(2T)$ quasienergy excitations ($T$ being the driving period), which have no static counterpart and arise from the interplay between interaction effect and periodic driving. At special parameter values, these exotic quasiparticles can be analytically and exactly derived. Strong numerical evidence of their robustness against variations in parameter values and spatial disorder is further presented. Our proposal offers a route toward realizing parafermions without fractional quantum Hall systems or complicated interactions.

arXiv comment14 pages, 5 figures. Published in PRB as a letter

References in corpus (87)

• Quantum Spin Hall Effect in Graphene
• Fault-tolerant quantum computation by anyons
• Quantum Spin Hall Effect and Topological Phase Transition in HgTe Quantum Wells
• Non-Abelian Anyons and Topological Quantum Computation
• Quantum Spin Hall Insulator State in HgTe Quantum Wells
• Unpaired Majorana fermions in quantum wires
• Electronic Structure of Pyrochlore Iridates: From Topological Dirac Metal to Mott Insulator
• Topological Insulators in Three Dimensions
• Topological Insulators with Inversion Symmetry
• Signatures of Majorana fermions in hybrid superconductor-semiconductor nanowire devices
• A topological Dirac insulator in a quantum spin Hall phase : Experimental observation of first strong topological insulator
• Majorana Fermions and a Topological Phase Transition in Semiconductor-Superconductor Heterostructures
• Classification of topological insulators and superconductors in three spatial dimensions
• Discovery of a Weyl Fermion Semimetal and Topological Fermi Arcs
• Helical liquids and Majorana bound states in quantum wires
• Novel Symmetry Classes in Mesoscopic Normal-Superconducting Hybrid Structures
• Topological invariants of time-reversal-invariant band structures
• Experimental realisation of the topological Haldane model
• Evidence of Majorana fermions in an Al - InAs nanowire topological superconductor
• Quantized Electric Multipole Insulators
• Experimental discovery of Weyl semimetal TaAs
• Non-Abelian statistics and topological quantum information processing in 1D wire networks
• Realization of the Hofstadter Hamiltonian with ultracold atoms in optical lattices
• Electric Multipole Moments, Topological Multipole Moment Pumping, and Chiral Hinge States in Crystalline Insulators
• Observation of the fractional ac Josephson effect: the signature of Majorana particles
• Observation of a Discrete Time Crystal
• Exponential Protection of Zero Modes in Majorana Islands
• Observation of discrete time-crystalline order in a disordered dipolar many-body system
• A Theory of Fault-Tolerant Quantum Computation
• Light-induced anomalous Hall effect in graphene
• Majorana Fermions in Equilibrium and Driven Cold Atom Quantum Wires
• Scalable Designs for Quasiparticle-Poisoning-Protected Topological Quantum Computation with Majorana Zero Modes
• Observation of topologically protected bound states in a one dimensional photonic system
• Spin-resolved Andreev levels and parity crossings in hybrid superconductor-semiconductor nanostructures
• Floquet topological insulators
• Scaling of Majorana Zero-Bias Conductance Peaks
• Exotic non-Abelian anyons from conventional fractional quantum Hall states
• Universal topological quantum computation from a superconductor/Abelian quantum Hall heterostructure
• Periodic Table for Floquet Topological Insulators
• Flux-controlled quantum computation with Majorana fermions
• Coulomb-assisted braiding of Majorana fermions in a Josephson junction array
• Parafermionic edge zero modes in Z_n-invariant spin chains
• A Majorana smoking gun for the superconductor-semiconductor hybrid topological system
• Topological singularities and the general classification of Floquet-Bloch systems
• Topological phases with parafermions: theory and blueprints
• Majorana box qubits
• Fractionalizing Majorana fermions: non-abelian statistics on the edges of abelian quantum Hall states
• A Short Introduction to Topological Quantum Computation
• Transport signatures of Floquet Majorana fermions in driven topological superconductors
• Generating Many Majorana Modes via Periodic Driving: A Superconductor Model
• Observation of anomalous π modes in photonic Floquet engineering
• Time-Reversal-Invariant $Z_4$ Fractional Josephson Effect
• Towards realistic implementations of a Majorana surface code
• Roadmap to Majorana surface codes
• Simulation of non-Abelian braiding in Majorana time crystals
• Floquet time crystals in clock models
• Floquet Majorana and Para-Fermions in Driven Rashba Nanowires
• Non-Abelian parafermions in time-reversal invariant interacting helical systems
• Topological Effects in Chiral Symmetric Driven Systems
• Floquet topological semimetal phases of an extended kicked Harper model
• Nonlinearity induced topological physics in momentum space and real space
• Non-Hermitian Floquet topological superconductors with multiple Majorana edge modes
• Quantum Computing with Majorana Fermion Codes
• Measurement-only quantum computation with Majorana corner modes
• Recipe for creating an arbitrary number of Floquet chiral edge states
• Quantum computation via Floquet topological edge modes
• Fractional Topological Superconductivity and Parafermion Corner States
• Braiding of Atomic Majorana Fermions in Wire Networks and Implementation of the Deutsch-Josza Algorithm
• Metaplectic Anyons, Majorana Zero Modes, and their Computational Power
• Aspects of Floquet Bands and Topological Phase Transitions in a Continuously Driven Superlattice
• Direct prediction of corner state configurations from edge winding numbers in 2D and 3D chiral-symmetric lattice systems
• Parafermion chain with $2\pi /k$ Floquet edge modes
• Time-induced second-order topological superconductors
• Z4 parafermions in one-dimensional fermionic lattices
• Fermionized parafermions and symmetry-enriched Majorana modes
• Generating controllable type-II Weyl points via periodic driving
• Majorana states in inhomogeneous spin ladders
• Nonlinear Dirac Cones
• Line nodes and surface Majorana flat bands in static and kicked p-wave superconducting Harper model
• Dissipative Floquet Majorana modes in proximity-induced topological superconductors
• Parafermion braiding in fractional quantum Hall edge states with finite chemical potential
• Topological and dynamical features of periodically driven spin ladders
• Nonlocal discrete time crystals in periodically driven surface codes
• Combating quasiparticle poisoning with multiple Majorana fermions in a periodically-driven quantum wire
• Measuring Majorana fermions qubit state and non-Abelian braiding statistics in quenched inhomogeneous spin ladders
• Braids and phase gates through high-frequency virtual tunneling of Majorana Zero Modes
• Time-periodic corner states from Floquet higher-order topology

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