Antiferromagnetic state in bilayer graphene

Motivated by the recent experiment of Velasco Jr. et al. [J. Velasco Jr. et al., Nat. Nanotechnology 7, 156 (2012)], we develop a mean-field theory of the interaction-induced antiferromagnetic (AF) state in bilayer graphene at charge neutrality point at arbitrary perpendicular magnetic field B. We demonstrate that the AF state can persist at all B. At higher B, the state continuously crosses over to the AF phase of the nu = 0 quantum Hall ferromagnet, recently argued to be realized in the insulating nu = 0 state. The mean-field quasiparticle gap is finite at B = 0 and grows with increasing B, becoming quasilinear in the quantum Hall regime, in accord with the reported behavior of the transport gap. By adjusting the two free parameters of the model, we obtain a simultaneous quantitative agreement between the experimental and theoretical values of the key parameters of the gap dependence-its zero-field value and slope at higher fields. Our findings suggest that the insulating state observed in bilayer graphene in Ref. 1 is antiferromagnetic (canted, once the Zeeman effect is taken into account) at all magnetic fields.