Fractional Charge and Spin States in Topological Insulator Constrictions

Abstract

We investigate theoretically properties of two-dimensional topological insulator constrictions both in the integer and fractional regimes. In the presence of a perpedicular magnetic field, the constriction functions as a spin filter with near-perfect efficiency and can be switched by electric fields only. Domain walls between different topological phases can be created in the constriction as an interface between tunneling, magnetic fields, charge density wave, or electron-electron interactions dominated regions. These domain walls host non-Abelian bound states with fractional charge and spin and result in degenerate ground states with parafermions. If a proximity gap is induced bound states give rise to an exotic Josephson current with 8$\pi$-peridiodicity.

References in corpus (34)

• Quantum Spin Hall Insulator State in HgTe Quantum Wells
• 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
• Topological Field Theory of Time-Reversal Invariant Insulators
• Evidence of Majorana fermions in an Al - InAs nanowire topological superconductor
• Observation of Majorana Fermions in Ferromagnetic Atomic Chains on a Superconductor
• Observation of Majorana Fermions in a Nb-InSb Nanowire-Nb Hybrid Quantum Device
• Nonlocal edge state transport in the quantum spin Hall state
• The Quantum Spin Hall Effect: Theory and Experiment
• Topological Phases of Noncentrosymmetric Superconductors: Edge States, Majorana Fermions, and the Non-Abelian Statistics
• Finite size effects of helical edge states in HgTe/CdTe quantum wells
• Exotic non-Abelian anyons from conventional fractional quantum Hall states
• Genons, twist defects, and projective non-Abelian braiding statistics
• Majorana edge states in interacting one-dimensional systems
• Fractionalizing Majorana fermions: non-abelian statistics on the edges of abelian quantum Hall states
• Superconducting Proximity Effect on the Edge of Fractional Topological Insulators
• Spin-selective Peierls transition in interacting one-dimensional conductors with spin-orbit interaction
• Transition from fractional to Majorana fermions in Rashba nanowires
• Time-Reversal-Invariant $Z_4$ Fractional Josephson Effect
• Kramers Pairs of Majorana Fermions and Parafermions in Fractional Topological Insulators
• Tunneling between edge states in a quantum spin Hall system
• Non-Abelian parafermions in time-reversal invariant interacting helical systems
• Giant spin orbit interaction due to rotating magnetic fields in graphene nanoribbons
• Fermionic and Majorana Bound States in Hybrid Nanowires with Non-Uniform Spin-Orbit Interaction
• Quantum Spin Hall Effect in Strip of Stripes Model
• Helical States in Curved Bilayer Graphene
• Fractional Fermions with Non-Abelian Statistics
• Cooper-Pair Injection into Quantum Spin Hall Insulators
• Integer and Fractional Quantum Anomalous Hall Effect in a Strip of Stripes Model
• Fractional Topological Insulators: from sliding Luttinger Liquids to Chern-Simons theory
• Helical nuclear spin order in a strip of stripes in the Quantum Hall regime
• Time reversal symmetry broken fractional topological phases at zero magnetic field
• Quantum charge pumping through fractional Fermions in charge density modulated quantum wires and Rashba nanowires

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• Second Order Topological Superconductivity in $\pi$-Junction Rashba Layers
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• Quasi-one-dimensional Quantum Anomalous Hall Systems as New Platforms for Scalable Topological Quantum Computation
• Fractional Topological Superconductivity and Parafermion Corner States
• Majorana bound states in semiconducting nanostructures
• Theory of time reversal topological superconductivity in double Rashba wires -- symmetries of Cooper pair and Andreev bound states
• Majorana Kramers pairs in Rashba double nanowires with interactions and disorder
• Helical Liquids in Semiconductors
• Non-Abelian braiding of Dirac fermionic modes using topological corner states in higher-order topological insulator
• Majorana bound states in topological insulators without a vortex
• Low-field Topological Threshold in Majorana Double Nanowires
• Coupled-wire constructions: a Luttinger liquid approach to topology
• ${\mathbb{Z}}_4$ parafermions in weakly interacting superconducting constrictions at the helical edge of quantum spin Hall insulators
• From fractional solitons to Majorana fermions in a paradigmatic model of topological superconductivity
• Double-frequency Aharonov-Bohm effect and non-Abelian braiding properties of Jackiw-Rebbi zero-mode
• Parafermion braiding in fractional quantum Hall edge states with finite chemical potential
• Formation and detection of Majorana modes in quantum spin Hall trenches
• Majorana Bound States in Double Nanowires with Reduced Zeeman Thresholds due to Supercurrents
• 3/2 Fractional Quantum Hall Plateau in Confined Two-Dimensional Electron Gas
• Parafermions in a Kagome lattice of qubits for topological quantum computation
• Quasiparticle poisoning effects on the dynamics of topological Josephson junctions
• Boundary edge networks induced by bulk topology
• Majorana zero modes and their bosonization
• Parafermions in a multilegged geometry: Towards a scalable parafermionic network
• Fabry-Pérot resonant vortices and magnetoconductance in topological insulator constrictions with magnetic barriers
• Bosonization for fermions and parafermions
• Rational boundary charge in one-dimensional systems with interaction and disorder
• Conductance of fractional Luttinger liquids at finite temperatures
• All-electric spin transistor based on a side-gate-modulated two-dimensional topological insulator
• Time-Reversal Invariant Topological Superconductivity in Planar Josephson Bijunction
• Majorana bound states in topological insulators with hidden Dirac points
• Supercurrent Reversal in Two-Dimensional Topological Insulators
• Clock model and parafermions in Rashba nanowires
• Fractional boundary charges with quantized slopes in interacting one- and two-dimensional systems
• Interaction Driven Floquet Engineering of Topological Superconductivity in Rashba Nanowires
• Transport signatures of a Floquet topological transition at the helical edge
• Insulating regime of an underdamped current-biased Josephson junction supporting ${\mathbb{Z}}_3$ and ${\mathbb{Z}}_4$ parafermions
• Engineering chiral edge states in 2D topological insulator/ferromagnetic insulator heterostructures
• Universal conductance dips and fractional excitations in a two-subband quantum wire
• Unified model for non-Abelian braiding of Majorana and Dirac fermion zero modes
• Assessing bound states in a one-dimensional topological superconductor: Majorana versus Tamm
• Non-Abelian Evolution of a Majorana Train in a Single Josephson Junction
• Quantum computation with hybrid parafermion-spin qubits
• Nonlocal Correlation Mediated by Weyl Orbits