Nature of the anomalous $4/13$ fractional quantum Hall effect in graphene

Abstract

Extensive fractional quantum Hall effect (FQHE) has been observed in graphene-based materials. Some of the observed fractions are anomalous in that FQHE has not been established at these fractions in conventional GaAs systems. One such fraction is $4/13$, where incompressibility has recently been reported in graphene [Kumar et al., Nat. Comm. 9, 2776 (2018)]. We propose a partonic wave function at $4/13$ and show it to be a viable candidate to describe the Coulomb ground state. Using the effective edge theory, we make predictions for experimentally measurable properties of the state.

arXiv comment6 pages, 3 figures

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• Real-space entanglement spectra of parton states in fractional quantum Hall systems
• Local density of states and particle entanglement in topological quantum fluids
• Competition between fractional quantum Hall liquid and electron solid phases in the Landau levels of multilayer graphene
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• Static structure factor and the dispersion of the Girvin-MacDonald-Platzman density mode for fractional quantum Hall fluids on the Haldane sphere
• Conformal field theory approach to parton fractional quantum Hall trial wave functions
• From frustration-free parent Hamiltonians to off-diagonal long-range order: Moore-Read and related states in second quantization
• Dispersion of neutral collective modes in partonic fractional quantum Hall states and its applications to paired states of composite fermions
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• Linking infinite bond-dimension matrix product states with frustration-free Hamiltonians
• Collective excitations of fractional quantum Hall states in monolayer graphene
• Dispersion of collective modes in spinful fractional quantum Hall states on the sphere
• Cascade of fractional quantum Hall states in 2D system