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arXiv · 0802.2546

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

Igor F. Herbut·Bitan Roy
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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.

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Igor F. Herbut, Bitan Roy. 2008-06-29. Quantum critical scaling in magnetic field near the Dirac point in graphene. https://doi.org/10.1103/physrevb.77.245438

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