Fractional Quantum Hall Effect in Graphene: Quantitative Comparison between Theory and Experiment

Abstract

The observation of extensive fractional quantum Hall states in graphene brings out the possibility of more accurate quantitative comparisons between theory and experiment than previously possible, because of the negligibility of finite width corrections. We obtain accurate phase diagram for differently spin-polarized fractional quantum Hall states, and also estimate the effect of Landau level mixing using the modified interaction pseudopotentials given in the literature. We find that the observed phase diagram is in good quantitative agreement with theory that neglects Landau level mixing, but the agreement becomes significantly worse when Landau level mixing is incorporated assuming that the corrections to the energies are linear in the Landau level mixing parameter $\lambda$. This implies that a first order perturbation theory in $\lambda$ is inadequate for the current experimental systems, for which $\lambda$ is typically on the order of or greater than one. We also test the accuracy of the composite-fermion theory and find that all lowest Landau level projection methods used in the literature are very accurate for the states of the form $n/(2n+1)$ but for the states at $n/(2n-1)$ the results are more sensitive to the projection method. An earlier prediction of an absence of spin transitions for the $n/(4n+1)$ states is confirmed by more rigorous calculations, and new predictions are made regarding spin physics for the $n/(4n-1)$ states.

15 pages, 8 figures (this version: references updated, typos fixed)

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• The electronic properties of graphene
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• Multicomponent fractional quantum Hall effect in graphene
• Particle-hole symmetry and the Pfaffian state
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• Particle-Hole Symmetry and the $\nu =5/2$ Quantum Hall State
• The Fractional Quantum Hall States of Dirac Electrons in Graphene
• Infinite density matrix renormalization group for multicomponent quantum Hall systems
• Fractional Quantum Hall Effect in Graphene
• Composite Fermions and Broken Symmetries in Graphene
• The Phase Diagram of the $\nu =5/2$ Fractional Quantum Hall Effect: Effects of Landau Level Mixing and Non-Zero Width
• Valley polarization and susceptibility of composite fermions around nu=3/2
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• The Effects of Landau level mixing on the fractional quantum Hall effect in monolayer Graphene
• Recent Experimental Progress of Fractional Quantum Hall Effect: 5/2 Filling State and Graphene
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• Phase Diagram of Fractional Quantum Hall Effect of Composite Fermions in Multi-Component Systems
• Landau level mixing in the nu=5/2 fractional quantum Hall state
• Density dependence of valley polarization energy for composite fermions
• Spin-Polarization of Composite Fermions and Particle-Hole Symmetry Breaking
• Fractional Quantum Hall Effect and Wigner Crystal of Two-Flux Composite Fermions
• Composite fermion valley polarization energies: Evidence for particle-hole asymmetry
• Contrast between spin and valley degrees of freedom
• Fractional Quantum Hall Effect in a Diluted Magnetic Semiconductor
• Phase diagram and edge states of the $\nu =5/2$ fractional quantum Hall state with Landau level mixing and finite well thickness

Cited by in corpus (60)

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• Prediction of a non-Abelian fractional quantum Hall state with $f$-wave pairing of composite fermions in wide quantum wells
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• Interplay between fractional quantum Hall liquid and crystal phases at low filling
• Landau-Level Mixing and Particle-Hole Symmetry Breaking for Spin Transitions in the 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
• Model States for a Class of Chiral Topological Order Interfaces
• 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
• Composite fermion pairing induced by Landau level mixing
• Interacting composite fermions: Nature of the 4/5, 5/7, 6/7, and 6/17 fractional quantum Hall states
• Real-space entanglement spectra of parton states in fractional quantum Hall systems
• Application of path-integral quantization to indistinguishable particle systems topologically confined by a magnetic field
• Theoretical phase diagram of two-component composite fermions in double layer graphene
• Nature of the anomalous $4/13$ fractional quantum Hall effect in graphene
• Theory of Competing Charge Density Wave, Kekule and Antiferromagnetic ordered Fractional Quantum Hall states in Graphene aligned with Boron Nitride
• Incompressible States of the Interacting Composite Fermions in Negative Effective Magnetic Fields at $\nu =4/13$, 5/17, and 3/10
• Tunnel transport and interlayer excitons in bilayer fractional quantum Hall systems
• Elementary Excitations in Fractional Quantum Hall Effect from Classical Constraints
• Revisiting excitation gaps in the fractional quantum Hall effect
• Splitting of Girvin-MacDonald-Platzman density wave and the nature of chiral gravitons in 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 $\nu =2+\frac{4}{11}$
• Fractional quantum Hall coexistence phases in higher Landau levels of graphene
• Incompressible Even Denominator Fractional Quantum Hall States in the Zeroth Landau Level of Monolayer Graphene
• Magnetic and Lattice Ordered Fractional Quantum Hall Phases in Graphene
• Spin and valley ordering of fractional quantum Hall states in monolayer graphene
• Study of partially polarized fractional quantum Hall states
• Entanglement scaling and charge fluctuations in a Fermi liquid of composite fermions
• Very high-energy collective states of partons in fractional quantum Hall liquids
• Fermionic symmetry-protected topological state in strained graphene
• Hetero-Orbital Two-Component Fractional Quantum Hall States in Bilayer Graphene
• Tunneling density of states, correlation energy, and spin polarization in the fractional quantum Hall regime
• Fractional Quantum Hall Effect in n=0 Landau Band of Graphene with Chern Number Matrix
• Dispersion of neutral collective modes in partonic fractional quantum Hall states and its applications to paired states of composite fermions
• Adiabatic Continuity of the Spinful Quantum Hall States
• Collective excitations of fractional quantum Hall states in monolayer graphene
• Interplay of superconducting, metallic, and crystalline states of composite fermions at $\nu =1/6$ in wide quantum wells
• Anomalous Transport Gaps of Fractional Quantum Hall Phases in Graphene Landau Levels are Induced by Spin-Valley Entangled Ground States
• Dispersion of collective modes in spinful fractional quantum Hall states on the sphere
• Topological states in double monolayer graphene
• Study of polarization of even-denominator fractional quantum Hall states in SU(4) Graphene
• Topological correlations and breaking of fermionic antisymmetry of electrons in FQHE