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 gap scales linearly, $\Delta E\sim 14 B[T]K, with magnetic field.
Categories: cond-mat.str-el cond-mat.mes-hall