Prediction of a non-Abelian fractional quantum Hall state with $f$-wave pairing of composite fermions in wide quantum wells

Abstract

We theoretically investigate the nature of the state at quarter filled lowest Landau level and predict that, as the quantum well width is increased, a transition occurs from the composite fermion Fermi sea into a novel non-Abelian fractional quantum Hall state that is topologically equivalent to $f$-wave pairing of composite fermions. This state is topologically distinct from the familiar $p$-wave paired Pfaffian state. We compare our calculated phase diagram with experiments and make predictions for many observable quantities.

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Cited by in corpus (47)

• Thirty Years of Composite Fermions and Beyond
• Wavefunctionology: The Special Structure of Certain Fractional Quantum Hall Wavefunctions
• Fractional Quantum Hall Effect at $\nu =2+4/9$
• A non-Abelian parton state for the $\nu =2+3/8$ fractional quantum Hall effect
• ${\mathbb{Z}}_n$ superconductivity of composite bosons and the $7/3$ fractional quantum Hall effect
• Transitions from Abelian composite fermion to non-Abelian parton fractional quantum Hall states in the zeroth Landau level of bilayer graphene
• A non-Abelian fractional quantum Hall state at $3/7$ filled Landau level
• Fractional quantum Hall effect with unconventional pairing in monolayer graphene
• Unconventional ${\mathbb{Z}}_n$ parton states at $\nu =7/3$: The role of finite width
• Even-Denominator Fractional Quantum Hall State at Filling Factor ν = 3/4
• Abelian parton state for the $\nu =4/11$ fractional quantum Hall effect
• Composite-fermion pairing at half and quarter filled lowest Landau level
• Local two-body parent Hamiltonians for the entire Jain sequence
• Composite fermion pairing induced by Landau level mixing
• Geometric Fluctuation of Conformal Hilbert Spaces and Multiple Graviton Modes in Fractional Quantum Hall Effect
• Real-space entanglement spectra of parton states in fractional quantum Hall systems
• Theoretical phase diagram of two-component composite fermions in double layer graphene
• Fractional Quantum Hall State at Filling Factor $\nu =1/4$ in Ultra-High-Quality GaAs 2D Hole Systems
• Parton wave function for the fractional quantum Hall effect at $\nu =6/17$
• Nature of the anomalous $4/13$ fractional quantum Hall effect in graphene
• Bardeen-Cooper-Schrieffer pairing of composite fermions
• Origin of the $\nu =1/2$ fractional quantum Hall effect in wide quantum wells
• Local density of states and particle entanglement in topological quantum fluids
• Prediction of non-Abelian fractional quantum Hall effect at $\nu =2+\frac{4}{11}$
• Fractional quantum Hall effect of partons and the nature of the 8/17 state in the zeroth Landau level of bilayer graphene
• Fractional quantum Hall effect at the filling factor $\nu =5/2$
• Paired fermions in strong magnetic fields and daughters of even-denominator Hall plateaus
• Adiabatic Construction of Hierarchical Quantum Hall States
• Identifying non-Abelian anyons with upstream noise
• Identification of topological order in the fractional quantum Hall state at $\nu =1/4$
• Valley-tunable, even-denominator fractional quantum Hall state in the lowest Landau level of an anisotropic system
• Developing fractional quantum Hall states at even-denominator fillings 1/6 and 1/8
• Static structure factor and the dispersion of the Girvin-MacDonald-Platzman density mode for fractional quantum Hall fluids on the Haldane sphere
• Phase diagram of compressible and paired states in the quarter-filled Landau level
• Unlocking new regimes in fractional quantum Hall effect with quaternions
• A novel planar back-gate design to control the carrier concentrations in GaAs-based double quantum wells
• Two-component parton fractional quantum Hall state in graphene
• From frustration-free parent Hamiltonians to off-diagonal long-range order: Moore-Read and related states in second quantization
• Very high-energy collective states of partons in fractional quantum Hall liquids
• 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
• Linking infinite bond-dimension matrix product states with frustration-free Hamiltonians
• Non-Abelian topological order with SO(5)${}_1$ chiral edge states
• Interplay of superconducting, metallic, and crystalline states of composite fermions at $\nu =1/6$ in wide quantum wells
• Repulsive-Interaction-Driven Topological Superconductivity in a Landau Level Coupled to an $s$-Wave Superconductor
• Crossover from Integer to Fractional Quantum Hall Effect
• Collapse of edge reconstruction in compressible Quantum Hall fluid within filling fraction range 2/3 to 1