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 $\left({\tilde{\Delta }}_0,B\right)$, 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, $\Delta E\sim 10B\left[\text{T}\right]\text{K}$, with magnetic field. The comparison of these results with recent experiments in bilayer graphene is presented.

Figure 1

(Color online) The static polarization function $4\pi \tilde{\Pi }\left(y\right)$.

Figure 2

(Color online) The phase diagram in the $\left({\tilde{\Delta }}_0,B\right)$ plane at $B_{\parallel }=0$. Here the effective ${\kappa }_{eff}=4.$

Figure 3

(Color online) The LLL energies of the solutions I (left panel) and II (right panel) as functions of $B$ with $B_{\parallel }=0$. Here ${\tilde{\Delta }}_0=0$ and ${\tilde{\Delta }}_0=5\text{K}$ for solution I and solution II, respectively.

Figure 4

(Color online) The dependence of the energy gaps of solutions I (left panel) and II (right panel) on the field $B_{\perp }$ for different angles. The parameter ${\tilde{\Delta }}_0=5\text{K}$ for both solutions I and II.