Antiferromagnetic state in bilayer graphene

Abstract

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 $\ensuremath{\nu}=0$ quantum Hall ferromagnet, recently argued to be realized in the insulating $\ensuremath{\nu}=0$ 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.