Energy gaps at neutrality point in bilayer graphene in a magnetic field

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 $({\tilde{\mathrm{\Delta }}}_0,B)$, where ${\tilde{\mathrm{\Delta }}}_0$ is a top-bottom gates voltage imbalance, is described. It is shown that the energy gap scales linearly, $\Delta E\sim 14 B[T]K, with magnetic field.