Parafermions, induced edge states and domain walls in the fractional quantum Hall effect spin transitions

Abstract

Search for parafermions and Fibonacci anyons, which are excitations obeying non-Abelian statistics, is driven both by the quest for deeper understanding of nature and prospects for universal topological quantum computation. However, physical systems that can host these exotic excitations are rare and hard to realize in experiments. Here we study the domain walls and the edge states formed in spin transitions in the fractional quantum Hall effect. Effective theory approach and exact diagonalization in a disk and torus geometries proves the existence of the counter-propagating edge modes with opposite spin polarizations at the boundary between the two neighboring regions of the two-dimensional electron liquid in spin-polarized and spin-unpolarized phases. By analytical and numerical analysis, we argue that these systems can host parafermions when coupled to an s-wave superconductor and are experimentally feasible. We investigate settings based on $\nu =\frac{2}{3}$, $\nu =\frac{4}{3}$ and $\nu =\frac{5}{3}$ spin transitions and analyze spin-flipping interactions that hybridize counter-propagating modes. Finally, we discuss spin-orbit interactions of composite fermions.

arXiv comment17 pages, 12 figures

References in corpus (31)

• Non-Abelian Anyons and Topological Quantum Computation
• Superconducting proximity effect and Majorana fermions at the surface of a topological insulator
• Unpaired Majorana fermions in quantum wires
• Paired states of fermions in two dimensions with breaking of parity and time-reversal symmetries, and the fractional quantum Hall effect
• New directions in the pursuit of Majorana fermions in solid state systems
• A generic new platform for topological quantum computation using semiconductor heterostructures
• Non-abelian statistics of half-quantum vortices in p-wave superconductors
• Non-Abelian statistics and topological quantum information processing in 1D wire networks
• Topological orders and Edge excitations in FQH states
• Exotic non-Abelian anyons from conventional fractional quantum Hall states
• Universal topological quantum computation from a superconductor/Abelian quantum Hall heterostructure
• Sharp and Smooth Boundaries of Quantum Hall Liquids
• Parafermionic edge zero modes in Z_n-invariant spin chains
• Topological phases with parafermions: theory and blueprints
• The two-eigenvalue problem and density of Jones representation of braid groups
• Edge reconstruction in the $\nu =2/3$ fractional quantum Hall state
• The Structure of Fractional Edge States: A Composite Fermion Approach
• Majorana zero modes on a necklace
• Resources Required for Topological Quantum Factoring
• Effective action of a compressible QH state edge: application to tunneling
• Topological Phase Transition in the $\nu =2/3$ Quantum Hall Effect
• Fractional Quantum Hall Effect in a Diluted Magnetic Semiconductor
• Edge Excitations of the $\nu =2/3$ Spin-Singlet Quantum Hall State
• Parafermion supporting platform based on spin transitions in the fractional quantum Hall effect regime
• Ground state and edge excitations of quantum Hall liquid at filling factor 2/3
• Microscopic Study of Edge Excitations of Spin-Polarized and Spin-Unpolarized $\nu =2/3$ Fractional Quantum Hall Effect
• Effective field theory for the bulk and edge states of quantum Hall states in unpolarized single layer and bilayer systems
• Mesoscopic transport in electrostatically-defined spin-full channels in quantum Hall ferromagnets
• Disorder-generated non-Abelions
• Numerical investigation of gapped edge states in fractional quantum Hall-superconductor heterostructures
• Electrostatic control of quantum Hall ferromagnetic transition, a step toward reconfigurable network of helical channels

Cited by in corpus (11)

• Transport in helical Luttinger liquids in the fractional quantum Hall regime
• Theory of Competing Charge Density Wave, Kekule and Antiferromagnetic ordered Fractional Quantum Hall states in Graphene aligned with Boron Nitride
• Model wavefunctions for interfaces between lattice Laughlin states
• Anomalous periodicity and parafermion hybridization in superconducting qubits
• Model wavefunctions for an interface between lattice Laughlin and Moore-Read states
• Parafermions in Moiré Minibands
• Disorder-induced topological superconductivity in a spherical quantum-Hall--superconductor hybrid
• Robust translational invariance in topological bands against lattice potentials and disorders
• Pseudospin Polarization of Composite Fermions under Uniaxial Strain
• Phases of Quasi-One-Dimensional Fractional Quantum (Anomalous) Hall - Superconductor Heterostructures
• Repulsive-Interaction-Driven Topological Superconductivity in a Landau Level Coupled to an $s$-Wave Superconductor