Stability of the k=3 Read-Rezayi state in chiral two-dimensional systems with tunable interactions

Abstract

The k=3 Read-Rezayi (RR) parafermion quantum Hall state hosts non-Abelian excitations which provide a platform for the universal topological quantum computation. Although the RR state may be realized at the filling factor ν=12/5 in GaAs-based two-dimensional electron systems, the corresponding quantum Hall state is weak and at present nearly impossible to study experimentally. Here we argue that the RR state can alternatively be realized in a class of chiral materials with massless and massive Dirac-like band structure. This family of materials encompasses monolayer and bilayer graphene, as well as topological insulators. We show that, compared to GaAs, these systems provide several important advantages in realizing and studying the RR state. Most importantly, the effective interactions can be tuned {\it in situ} by varying the external magnetic field, and by designing the dielectric environment of the sample. This tunability enables the realization of RR state with controllable energy gaps in different Landau levels. It also allows one to probe the quantum phase transitions to other compressible and incompressible phases.

12 pages, 5 figures; to appear in New Journal of Physics, Focus on Topological Quantum Computation

References in corpus (18)

• The electronic properties of graphene
• Non-Abelian Anyons and Topological Quantum Computation
• Unconventional quantum Hall effect and Berry's phase of 2pi in bilayer graphene
• Quantum Hall Ferromagnetism in Graphene
• Multicomponent fractional quantum Hall effect in graphene
• Particle-hole symmetry and the Pfaffian state
• Particle-Hole Symmetry and the $\nu =5/2$ Quantum Hall State
• Fractional Quantum Hall States and Jack Polynomials
• Single valley Dirac fermions in zero-gap HgTe quantum wells
• Quantum Hall effect and Landau level crossing of Dirac fermions in trilayer graphene
• Electron interactions in graphene in a strong magnetic field
• The Fractional Quantum Hall States of Dirac Electrons in Graphene
• Fractional Quantum Hall Hierarchy and the Second Landau Level
• Topological Quantum Computing with Read-Rezayi States
• Spontaneous Particle-Hole Symmetry Breaking in the $\nu =5/2$ Fractional Quantum Hall Effect
• Tunable interactions and phase transitions in Dirac materials in a magnetic field
• Interaction-tuned compressible-to-incompressible phase transitions in the quantum Hall systems
• Atypical Fractional Quantum Hall Effect in Graphene at Filling Factor 1/3

Cited by in corpus (6)

• Spin-helical transport in normal and superconducting topological insulators
• Topological Phases in the Zeroth Landau Level of Bilayer Graphene
• Understanding degenerate ground states of a protected quantum circuit in the presence of disorder
• Focus on topological quantum computation
• Competition between fractional quantum Hall liquid and electron solid phases in the Landau levels of multilayer graphene
• Quantum Hall ferroelectric helix in bilayer graphene