Theory of integer quantum Hall effect in insulating bilayer graphene

Abstract

A variational ground state for insulating bilayer graphene (BLG), subject to quantizing magnetic fields, is proposed. Due to the Zeeman coupling, the layer anti-ferromagnet (LAF) order parameter in fully gapped BLG gets projected onto the spin easy plane, and simultaneously a ferromagnet order, which can further be enhanced by exchange interaction, develops in the direction of the magnetic field. The activation gap for the $\nu=0$ Hall state then displays a crossover from quadratic to linear scaling with the magnetic field, as it gets stronger, and I obtain excellent agreement with a number of recent experiments with realistic strengths for the ferromagnetic interaction. A component of the LAF order, parallel to the external magnetic field, gives birth to additional incompressible Hall states at filling $\nu=\pm 2$, whereas the remote hopping in BLG yields $\nu=\pm 1$ Hall states. Evolution of the LAF order in tilted magnetic fields, scaling of the gap at $\nu=2$, the effect of external electric fields on various Hall plateaus, and different possible hierarchies of fractional quantum Hall states are highlighted.