Even denominator fractional quantum Hall states in higher Landau levels of graphene

Abstract

An important development in the field of the fractional quantum Hall effect has been the proposal that the 5/2 state observed in the Landau level with orbital index $n=1$ of two dimensional electrons in a GaAs quantum well originates from a chiral $p$-wave paired state of composite fermions which are topological bound states of electrons and quantized vortices. This state is theoretically described by a "Pfaffian" wave function or its hole partner called the anti-Pfaffian, whose excitations are neither fermions nor bosons but Majorana quasiparticles obeying non-Abelian braid statistics. This has inspired ideas on fault-tolerant topological quantum computation and has also instigated a search for other states with exotic quasiparticles. Here we report experiments on monolayer graphene that show clear evidence for unexpected even-denominator fractional quantum Hall physics in the $n=3$ Landau level. We numerically investigate the known candidate states for the even-denominator fractional quantum Hall effect, including the Pfaffian, the particle-hole symmetric Pfaffian, and the 221-parton states, and conclude that, among these, the 221-parton appears a potentially suitable candidate to describe the experimentally observed state. Like the Pfaffian, this state is believed to harbour quasi-particles with non-Abelian braid statistics

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Cited by in corpus (81)

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• Fractional quantum Hall effect in CVD-grown graphene
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• Transitions from Abelian composite fermion to non-Abelian parton fractional quantum Hall states in the zeroth Landau level of bilayer graphene
• The sixteenfold way and the quantum Hall effect at half-integer filling factors
• Excellent electronic transport in heterostructures of graphene and monoisotopic boron-nitride grown at atmospheric pressure
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• A non-Abelian fractional quantum Hall state at $3/7$ filled Landau level
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• Thermal conductance and noise of Majorana modes along interfaced $\nu =5/2$ fractional quantum Hall states
• Composite fermion pairing induced by Landau level mixing
• Real-space entanglement spectra of parton states in fractional quantum Hall systems
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• Theoretical phase diagram of two-component composite fermions in double layer graphene
• Nature of the anomalous $4/13$ fractional quantum Hall effect in graphene
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• Anomalous Nematic States in High Half-Filled Landau Levels
• Topological characterization of hierarchical fractional quantum Hall effects in topological flat bands with SU($N$) symmetry
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• Fingerprints of anti-Pfaffian topological order in quantum point contact transport
• Theory of broken symmetry quantum Hall states in the $N=1$ Landau level of Graphene
• Fractional quantum Hall effect of partons and the nature of the 8/17 state in the zeroth Landau level of bilayer graphene
• Paired fermions in strong magnetic fields and daughters of even-denominator Hall plateaus
• Emergent QCD${}_3$ Quantum Phase Transitions of Fractional Chern Insulators
• Fractional quantum Hall effect at the filling factor $\nu =5/2$
• Competition of Pairing and Nematicity in the Two-Dimensional Electron Gas
• Prediction of non-Abelian fractional quantum Hall effect at $\nu =2+\frac{4}{11}$
• Identifying non-Abelian anyons with upstream noise
• Adiabatic Construction of Hierarchical Quantum Hall States
• Orbitally controlled quantum Hall states in decoupled two-bilayer graphene sheets
• Identification of topological order in the fractional quantum Hall state at $\nu =1/4$
• Observation of 1/3 fractional quantum Hall physics in balanced large angle twisted bilayer graphene
• Conformal field theory approach to parton fractional quantum Hall trial wave functions
• Magnetic and Lattice Ordered Fractional Quantum Hall Phases in Graphene
• Phase diagram of compressible and paired states in the quarter-filled Landau level
• Fractional quantum Hall coexistence phases in higher Landau levels of graphene
• Energy minimization of paired composite fermion wave functions in the spherical geometry
• Non-linear Landau fan diagram for graphene electrons exposed to a moiré potential
• Two-component parton fractional quantum Hall state in graphene
• Very high-energy collective states of partons in fractional quantum Hall liquids
• Fractional quantum Hall state at $\nu =1/2$ with energy gap up to 6 K, and possible transition from one- to two-component state
• Disorder-induced topological superconductivity in a spherical quantum-Hall--superconductor hybrid
• Universal charge conductance at Abelian--non-Abelian quantum Hall interfaces
• Dispersion of neutral collective modes in partonic fractional quantum Hall states and its applications to paired states of composite fermions
• Non-Abelian phases from the condensation of Abelian anyons
• Phase transitions and topological properties of the 5/2 quantum Hall states with strong Landau-level mixing
• Anomalous Transport Gaps of Fractional Quantum Hall Phases in Graphene Landau Levels are Induced by Spin-Valley Entangled Ground States
• Interplay of superconducting, metallic, and crystalline states of composite fermions at $\nu =1/6$ in wide quantum wells
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