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.

6 pages, 3 figures

References in corpus (22)

• The electronic properties of graphene
• Multicomponent fractional quantum Hall effect in graphene
• Ultra-high quality two-dimensional electron systems
• Composite Fermions and Broken Symmetries in Graphene
• Spinful Composite Fermions in a Negative Effective Field
• Vanishing thermal equilibration for hole-conjugate fractional quantum Hall states in graphene
• Fractional Quantum Hall Effect at Landau Level Filling nu=4/11
• Prediction of a non-Abelian fractional quantum Hall state with $f$-wave pairing of composite fermions in wide quantum wells
• Phase Diagram of Fractional Quantum Hall Effect of Composite Fermions in Multi-Component Systems
• Observation of Incompressibility at $\nu =4/11$ and $\nu =5/13$
• Parton construction of particle-hole-conjugate Read-Rezayi parafermion fractional quantum Hall states and beyond
• Fractional Quantum Hall Effect at $\nu =2+4/9$
• A non-Abelian parton state for the $\nu =2+3/8$ 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
• Unconventional ${\mathbb{Z}}_n$ parton states at $\nu =7/3$: The role of finite width
• Abelian parton state for the $\nu =4/11$ fractional quantum Hall effect
• Interacting composite fermions: Nature of the 4/5, 5/7, 6/7, and 6/17 fractional quantum Hall states
• Particle-hole symmetry for composite fermions: An emergent symmetry in the fractional quantum Hall effect
• Parton wave function for the fractional quantum Hall effect at $\nu =6/17$
• Anomalously low magnetoroton energies of the unconventional fractional quantum Hall states of composite fermions
• Unconventional Filling Factor 4/11: A Closed-Form Ground State Wave Function

Cited by in corpus (14)

• 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
• 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
• 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
• Numerical demonstration of Abelian fractional statistics of composite fermions in the spherical geometry
• 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