Generalized parafermions and non-local Josephson effect in multi-layer systems

Abstract

We theoretically investigate the effects of backscattering and superconducting proximity terms between the edges of two multi-layer fractional quantum Hall (FQH) systems. While the different layers are strongly interacting, we assume that tunneling between them is absent. Studying the boundaries between regions gapped by the two mechanisms in an $N$-layer system, we find $N$ localized zero-mode operators realizing a generalized parafermionic algebra. We further propose an experiment capable of probing imprints of the generalized parafermionic bound states. This is done by coupling different superconducting contacts to different layers, and examining the periodicity of the Josephson effect as a function of the various relative superconducting phases. Remarkably, even if we apply a phase difference between the superconductors in one layer, we induce a Josephson current at the other layers due to inter-layer interactions. Furthermore, while the Josephson effect is commonly used to probe only charged degrees of freedom, the possibility of independently controlling the superconducting phase differences between the layers allows us to find imprints of the neutral modes of the underlying multi-layer system. In particular, we propose two configurations, one of which is capable of isolating the signal associated with the charge modes, while the other probes the neutral modes.

13 pages, 5 figures

References in corpus (65)

• Superconducting proximity effect and Majorana fermions at the surface of a topological insulator
• Signatures of Majorana fermions in hybrid superconductor-semiconductor nanowire devices
• Majorana Fermions and a Topological Phase Transition in Semiconductor-Superconductor Heterostructures
• Helical liquids and Majorana bound states in quantum wires
• New directions in the pursuit of Majorana fermions in solid state systems
• Evidence of Majorana fermions in an Al - InAs nanowire topological superconductor
• Search for Majorana fermions in superconductors
• Observation of Majorana Fermions in a Nb-InSb Nanowire-Nb Hybrid Quantum Device
• Observation of the Fractional Quantum Hall Effect in Graphene
• Beyond paired quantum Hall states: parafermions and incompressible states in the first excited Landau level
• Fractional quantum Hall effect and insulating phase of Dirac electrons in graphene
• Superconductor-Nanowire Devices from Tunneling to the Multichannel Regime: Zero-Bias Oscillations and Magnetoconductance Crossover
• Single Layer Behavior and Its Breakdown in Twisted Graphene Layers
• Multicomponent fractional quantum Hall effect in graphene
• Exotic non-Abelian anyons from conventional fractional quantum Hall states
• Universal topological quantum computation from a superconductor/Abelian quantum Hall heterostructure
• Towards identification of a non-abelian state: observation of a quarter of electron charge at $\nu =5/2$ quantum Hall state
• Genons, twist defects, and projective non-Abelian braiding statistics
• The Fractional Quantum Hall effect in an array of quantum wires
• Measurement of filling factor 5/2 quasiparticle interference: observation of charge e/4 and e/2 period oscillations
• From Luttinger liquid to non-Abelian quantum Hall states
• Topological Nematic States and Non-Abelian Lattice Dislocations
• Fractionalizing Majorana fermions: non-abelian statistics on the edges of abelian quantum Hall states
• Superconducting Proximity Effect on the Edge of Fractional Topological Insulators
• Observation of neutral modes in the fractional quantum Hall regime
• Unconventional Sequence of Fractional Quantum Hall States in Suspended Graphene
• Theory of defects in Abelian topological states
• Time-Reversal Invariant Parafermions in Interacting Rashba Nanowires
• Unraveling the spin polarization of the v = 5/2 fractional quantum Hall state
• Time-Reversal-Invariant $Z_4$ Fractional Josephson Effect
• Wire deconstructionism of two-dimensional topological phases
• Electron-Hole Asymmetric Integer and Fractional Quantum Hall Effect in Bilayer Graphene
• Fractional Helical Liquids and Non-Abelian Anyons in Quantum Wires
• Local Charge of the nu=5/2 Fractional Quantum Hall State
• Theory of interacting topological crystalline insulators
• Parafermions in Interacting Nanowire Bundle
• Non-Abelian parafermions in time-reversal invariant interacting helical systems
• Coupled wire construction of chiral spin liquids
• Measurement of the ν= 1/3 fractional quantum Hall energy gap in suspended graphene
• Superconducting analogue of the parafermion fractional quantum Hall states
• Non-Abelian topological insulators from an array of quantum wires
• Chiral Spin Liquids in Arrays of Spin Chains
• NMR probing of the spin polarization of the nu=5/2 quantum Hall state
• Experimental probe of topological orders and edge excitations in the second Landau level
• Quantum Spin Hall Effect in Strip of Stripes Model
• Measurements of quasi-particle tunneling in the nu = 5/2 fractional quantum Hall state
• Topological Superconducting Phases of Weakly Coupled Quantum Wires
• Fibonacci Anyons From Abelian Bilayer Quantum Hall States
• Composite Dirac liquids: parent states for symmetric surface topological order
• Optical Probing of the Spin Polarization of the nu=5/2 Quantum Hall State
• Non-Abelian topological spin liquids from arrays of quantum wires or spin chains
• Rapid collapse of spin waves in non-uniform phases of the second Landau level
• Fractional Topological Insulators: from sliding Luttinger Liquids to Chern-Simons theory
• Topological Edge States and Fractional Quantum Hall Effect from Umklapp Scattering
• Thermoelectric response of fractional quantized Hall and re-entrant insulating states in the N=1 Landau level
• Wire constructions of Abelian topological phases in three or more dimensions
• From an array of quantum wires to three-dimensional fractional topological insulators
• Fractional topological phases in three-dimensional coupled-wire systems
• Coupled wire model of symmetric Majorana surfaces of topological superconductors
• Imprint of topological degeneracy in quasi-one-dimensional fractional quantum Hall states
• Time reversal symmetry broken fractional topological phases at zero magnetic field
• Theory of a 3+1D fractional chiral metal: interacting variant of the Weyl semimetal
• Blockade and Counterflow Supercurrent in exciton-condensate Josephson junctions
• Bridging coupled wires and lattice Hamiltonian for two-component bosonic quantum Hall states
• Josephson current in a four terminal superconductor - exciton condensate - superconductor system

Cited by in corpus (9)

• Coupled-wire constructions: a Luttinger liquid approach to topology
• Non-topological parafermions in a one-dimensional fermionic model with even multiplet pairing
• Bosonization for fermions and parafermions
• Numerical investigation of gapped edge states in fractional quantum Hall-superconductor heterostructures
• Dynamical topological excitations in parafermion chains
• Unusual Superconducting Proximity Effect in Magnetically Doped Topological Josephson Junctions
• Enhancement in tunneling density of states in Luttinger liquid -- role of non-local interaction
• Manifestation of edge-bulk incompatibility in fractional quantum Hall platform
• Phases of Quasi-One-Dimensional Fractional Quantum (Anomalous) Hall - Superconductor Heterostructures