Dynamics and phase diagram of theν=0quantum Hall state in bilayer graphene

Abstract

Utilizing the Baym-Kadanoff formalism with the polarization function calculated in the random phase approximation, the dynamics of the $\ensuremath{\nu}=0$ 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 $({\stackrel{\ifmmode \tilde{}\else \~{}\fi{}}{\ensuremath{\Delta}}}_{0},B)$, where ${\stackrel{\ifmmode \tilde{}\else \~{}\fi{}}{\ensuremath{\Delta}}}_{0}$ is a top-bottom gates voltage imbalance, is described. It is shown that the energy gaps in these phases scale linearly, $\ensuremath{\Delta}E\ensuremath{\sim}10B\text{ }[\text{T}]\text{K}$, with magnetic field. The comparison of these results with recent experiments in bilayer graphene is presented.