Dynamics and phase diagram of the $\nu=0$ quantum Hall state in bilayer graphene

Utilizing the Baym-Kadanoff formalism with the polarization function calculated in the random phase approximation, the dynamics of the $\nu=0$ quantum Hall state in bilayer graphene is analyzed. Two phases with nonzero energy gap, the ferromagnetic and layer asymmetric ones, are found. The phase diagram in the plane $(\tilde{\Delta}_0,B)$, where $\tilde{\Delta}_0$ is a top-bottom gates voltage imbalance, is described. It is shown that the energy gaps in these phases scale linearly, $\Delta E\sim 10 B[T]K, with magnetic field. The comparison of these results with recent experiments in bilayer graphene is presented.