Instabilities of the $AA$-Stacked Graphene Bilayer

Tight-binding calculations predict that the $AA$-stacked bilayer graphene has one electron and one hole conducting band, and that the Fermi surfaces of these bands coincide. We demonstrate that as a result of this degeneracy, the bilayer becomes unstable with respect to a set of spontaneous symmetry violations. Which of the symmetries is broken depends on the microscopic details of the system. For strong on-site Coulomb interaction we find that antiferromagnetism is the most stable order parameter. For an on-site repulsion energy typical for graphene systems, the antiferromagnetic gap can exist up to room temperature.

Figure 1

(a) The band structure of the $AA$-stacked bilayer graphene. (b) The $\mathbf{k}$-dependence of the spectra ${\epsilon }_{\mathbf{k}}^{(s)}$ near the Dirac point $\mathcal{K}$ located at momentum $\mathbf{K}$; $\mathbf{k}=\mathbf{K}+\delta k_y{\mathbf{e}}_y$. Bands $s=2$ and $s=3$ intersect at the Fermi level (${\epsilon }_{\mathrm{F}}\approx -0.004\mathrm{eV}$). (c) Solid (green) arcs show six fragments of the Fermi surface in the first Brillouin zone.

Figure 2

AFM gap $\Delta$ at $T=0$ (left $y$ axis) and crossover temperature $T^{*}$ (right $y$ axis) versus the on-site Coulomb repulsion $U$. The solid (red) curve is calculated by solving Eq. (15), while the dashed (blue) curve is calculated from Eq. (16). The crossover temperature $T^{*}$ is proportional to $\Delta$. The figure can be considered as a phase diagram in the $U\mathrm{\text{−}}T$ plane, where the solid (red) curve separates the AFM short-range order phase from the paramagnetic metallic phase. The inset shows the electron spectrum near the $\mathcal{K}$ point at $U=5.5\mathrm{eV}$ ($\Delta \approx 0.12\mathrm{eV}$).