Transitions from Abelian composite fermion to non-Abelian parton fractional quantum Hall states in the zeroth Landau level of bilayer graphene

Abstract

The electron-electron interaction in the Landau levels of bilayer graphene is markedly different from that of conventional semiconductors such as GaAs. We show that in the zeroth Landau level of bilayer graphene, in the orbital which is dominated by the non-relativistic second Landau level wave function, by tuning the magnetic field a topological quantum phase transition from an Abelian composite fermion to a non-Abelian parton fractional quantum Hall state can be induced at filling factors $1/2,2/5$ and $3/7$. The parton states host exotic anyons that can potentially be utilized to store and process quantum information. Intriguingly, some of these transitions may have been observed in a recent experiment [Huang \emph{et al.} arXiv:2105.07058].

arXiv commentmain text: 4 pages, 2 figures includes supplemental material (published version)

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• Energy gap of the even-denominator fractional quantum Hall state in bilayer graphene
• Fractional quantum Hall effect with unconventional pairing in monolayer graphene
• Composite-fermion pairing at half and quarter filled lowest Landau level
• Composite fermion pairing induced by Landau level mixing
• Real-space entanglement spectra of parton states in fractional quantum Hall systems
• Nature of the anomalous $4/13$ fractional quantum Hall effect in graphene
• Aharonov-Bohm oscillations in bilayer graphene edge state Fabry-Pérot interferometers
• Local density of states and particle entanglement in topological quantum fluids
• Revisiting excitation gaps in the fractional quantum Hall effect
• Competition between fractional quantum Hall liquid and electron solid phases in the Landau levels of multilayer graphene
• Fractional quantum Hall effect of partons and the nature of the 8/17 state in the zeroth Landau level of bilayer graphene
• Prediction of non-Abelian fractional quantum Hall effect at $\nu =2+\frac{4}{11}$
• Magnetic and Lattice Ordered Fractional Quantum Hall Phases in Graphene
• Unlocking new regimes in fractional quantum Hall effect with quaternions
• Static structure factor and the dispersion of the Girvin-MacDonald-Platzman density mode for fractional quantum Hall fluids on the Haldane sphere
• Fractional quantum Hall coexistence phases in higher Landau levels of graphene
• Very high-energy collective states of partons in fractional quantum Hall liquids
• Hetero-Orbital Two-Component Fractional Quantum Hall States in Bilayer Graphene
• Numerical demonstration of Abelian fractional statistics of composite fermions in the spherical geometry
• Dispersion of neutral collective modes in partonic fractional quantum Hall states and its applications to paired states of composite fermions
• Exploring the nature of the emergent gauge field in composite-fermion metals: A large-scale microscopic study
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• Composite fermions and parton wavefunctions in twisted graphene on hexagonal boron nitride