Theory of integer quantum Hall effect in insulating bilayer graphene

Abstract

A variational ground state for insulating bilayer graphene (BLG), subject to quantizing magnetic fields, is proposed. Due to the Zeeman coupling, the layer anti-ferromagnet (LAF) order parameter in fully gapped BLG gets projected onto the spin easy plane, and simultaneously a ferromagnet order, which can further be enhanced by exchange interaction, develops in the direction of the magnetic field. The activation gap for the $\nu =0$ Hall state then displays a crossover from quadratic to linear scaling with the magnetic field, as it gets stronger, and I obtain excellent agreement with a number of recent experiments with realistic strengths for the ferromagnetic interaction. A component of the LAF order, parallel to the external magnetic field, gives birth to additional incompressible Hall states at filling $\nu =\pm 2$, whereas the remote hopping in BLG yields $\nu =\pm 1$ Hall states. Evolution of the LAF order in tilted magnetic fields, scaling of the gap at $\nu =2$, the effect of external electric fields on various Hall plateaus, and different possible hierarchies of fractional quantum Hall states are highlighted.

Published version: 5 pages, 2 figures (Supplementary: 6 pages, 2 figures); New references, typos corrected

References in corpus (23)

• Unconventional Integer Quantum Hall effect in graphene
• Transport Spectroscopy of Symmetry-Broken Insulating States in Bilayer Graphene
• Theory of interacting electrons on the honeycomb lattice
• Determination of the electronic structure of bilayer graphene from infrared spectroscopy results
• Dissipative Quantum Hall Effect in Graphene near the Dirac Point
• Evidence for a Spin Phase Transition at ν=0 in Bilayer Graphene
• Local Compressibility Measurements of Correlated States in Suspended Bilayer Graphene
• Theory of integer quantum Hall effect in graphene
• Unconventional superconductivity on honeycomb lattice: the theory of Kekule order parameter
• Interacting fermions on the honeycomb bilayer: from weak to strong coupling
• SO(3) symmetry between Neel and ferromagnetic order parameters for graphene in a magnetic field
• Antiferromagnetic state in bilayer graphene
• Fermions on bilayer graphene: symmetry breaking for B=0 and nu=0
• Edge states, mass and spin gaps, and quantum Hall effect in graphene
• Dynamics and phase diagram of the $\nu =0$ quantum Hall state in bilayer graphene
• Composite Dirac fermions in graphene
• Broken-symmetry $\nu =0$ quantum Hall states in bilayer graphene: Landau level mixing and dynamical screening
• Quantum critical scaling in magnetic field near the Dirac point in graphene
• Topological insulators in strained graphene at weak interaction
• Broken-symmetry states and phase diagram of the lowest Landau level in bilayer graphene
• Spin Symmetry of the Bilayer Graphene Groundstate
• Classification of massive and gapless phases in bilayer graphene
• Homogeneity of Bilayer Graphene

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• Chiral Symmetry Breaking and the Quantum Hall Effect in Monolayer Graphene
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• Zero-modes and global antiferromagnetism in strained graphene
• Distinct Competing Ordered ν=2 States in Bilayer Graphene
• Edge structure of graphene monolayers in the ν = 0 quantum Hall state
• Spin-Valley Coherent Phases of the $\nu =0$ Quantum Hall State in Bilayer Graphene
• Thermal Transport Signatures of Broken-Symmetry Phases in Graphene
• Phase diagram of a graphene bilayer in the zero-energy Landau level
• Deconfined criticality in bilayer graphene
• Ferromagnetism and glassiness on the surface of topological insulators
• Incompressible Even Denominator Fractional Quantum Hall States in the Zeroth Landau Level of Monolayer Graphene
• Color degeneracy of competing orders near topological defects cores in planar quadratic band touching systems
• Spontaneous symmetry breaking and quantum Hall valley ordering on the surface of topological hexaborides
• Non-Hermitian catalysis of spontaneous symmetry breaking on Euclidean and hyperbolic lattices
• Broken symmetry states in bilayer graphene in electric and in-plane magnetic fields
• Interacting quantum Hall states in a finite graphene flake and at finite temperature
• Collective excitations of fractional quantum Hall states in monolayer graphene
• Dynamical polarization in ABC-stacked multilayer graphene in a magnetic field