Quantum critical scaling in magnetic field near the Dirac point in graphene

Abstract

Motivated by the recent measurement of the activation energy at the quantum Hall state at the filling factor f=1 in graphene we discuss the scaling of the interaction-induced gaps in vicinity of the Dirac point with the magnetic field. The gap at f=1 is shown to be bounded from above by E(1)/C, where E(n) are the Landau level energies and C = 5.985 + O(1/N) is a universal number. The universal scaling functions are computed exactly for a large number of Dirac fermions N. We find a sublinear dependence of the gap at the laboratory magnetic fields for realistic values of short-range repulsion between electrons, and in quantitative agreement with observation.

arXiv comment5 RevTex pages, 3 figures; added comments and references; cosmetic changes (this, published, version)

References in corpus (25)

• Two-Dimensional Gas of Massless Dirac Fermions in Graphene
• Experimental Observation of Quantum Hall Effect and Berry's Phase in Graphene
• Detection of Individual Gas Molecules Absorbed on Graphene
• Unconventional Integer Quantum Hall effect in graphene
• Quantum Hall Ferromagnetism in Graphene
• Landau Level Splitting in Graphene in High Magnetic Fields
• Non-Fermi liquid behaviour of electrons in the half-filled honeycomb lattice (A renormalization group approach)
• Interactions and phase transitions on graphene's honeycomb lattice
• Marginal Fermi liquid behavior from 2d Coulomb interaction
• The Nature of Quantum Hall States near the Charge Neutral Dirac Point in Graphene
• Quantum critical scaling in graphene
• Quantum critical point in graphene approached in the limit of infinitely strong Coulomb interaction
• Coulomb Interactions and Ferromagnetism in Pure and Doped Graphene
• Dynamical Flavor Symmetry Breaking by a Magnetic Field in $2+1$ Dimensions
• Coulomb interaction, ripples, and the minimal conductivity of graphene
• Electron interactions in graphene in a strong magnetic field
• Excitonic gap, phase transition, and quantum Hall effect in graphene
• Theory of integer quantum Hall effect in graphene
• Spontaneous parity breaking of graphene in the quantum Hall regime
• Critical exponents of the Gross-Neveu model from the effective average action
• SO(3) symmetry between Neel and ferromagnetic order parameters for graphene in a magnetic field
• Spontaneous Symmetry Breaking and Quantum Hall Effect in Graphene
• Anomalous thermodynamics of Coulomb interacting massless Dirac fermions in two spatial dimensions
• Renormalization group approach to 2D Coulomb interacting Dirac fermions with random gauge potential
• Quantum critical points with the Coulomb interaction and the dynamical exponent: when and why z=1

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