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Abstract: Motivated by the recent measurement of the activation energy at the quantumHall state at the filling factor f=1 in graphene we discuss the scaling of theinteraction-induced gaps in vicinity of the Dirac point with the magneticfield. The gap at f=1 is shown to be bounded from above by E1-C, where Enare the Landau level energies and C = 5.985 + O1-N is a universal number. Theuniversal scaling functions are computed exactly for a large number of Diracfermions N. We find a sublinear dependence of the gap at the laboratorymagnetic fields for realistic values of short-range repulsion betweenelectrons, and in quantitative agreement with observation.



Author: Igor F. Herbut, Bitan Roy

Source: https://arxiv.org/



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