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.

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

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• Dynamics in the quantum Hall effect and the phase diagram of graphene
• Chiral Symmetry Breaking and the Quantum Hall Effect in Monolayer Graphene
• Pseudo-magnetic catalysis of the time-reversal symmetry breaking in graphene
• Collective modes and Kosterlitz-Thouless transition in a magnetic field in the planar Nambu--Jona-Lasino model
• Competing charge-density-wave, magnetic and topological ground states at and near Dirac points in graphene in axial magnetic fields
• Influence of spatially varying pseudo-magnetic field on a 2D electron gas in graphene
• Quantum criticality of magnetic catalysis in two-dimensional correlated Dirac fermions
• The magnetized (2+1)-dimensional Gross-Neveu model at finite density
• Dirac Kondo effect under magnetic catalysis
• Collective excitations of fractional quantum Hall states in monolayer graphene
• The Hubbard Model on the Honeycomb Lattice with Hybrid Monte Carlo