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

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

2008-02-18

arxiv.org/abs/0802.2546v3

Phys. Rev. B vol. 77, 245438 (2008)

Physics

Condensed Matter

Mesoscale and Nanoscale Physics

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

Scientific paper

10.1103/PhysRevB.77.245438

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.

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