We show that two graphene layers stacked directly on top of each other ($AA$ stacking) form strong chemical bonds when the distance between planes is $0.156\mathrm{nm}$. Simultaneously, C–C in-plane bonds are considerably weakened from partial double bond $\left(0.141\mathrm{nm}\right)$ to single bond $\left(0.154\mathrm{nm}\right)$. This polymorphic form of graphene bilayer is metastable with an activation energy of $0.16\mathrm{eV}∕\text{cell}$ with respect to the standard configuration bound by van der Waals forces at a larger separation between planes $\left(0.335\mathrm{nm}\right)$. Carbon atoms form four single bonds in a geometry mixing 90° and 120° angles, intermediate between the usual $s{p}^2$ and $s{p}^3$, but similar to the one found in molecules like the cubane, pentaprismane, or hexaprismane. Under an in-plane stress of $9\mathrm{GPa}$, this carbon allotrope becomes the global energy minimum. As a function of the separation between layers, the electronic band structure goes through different regimes: It is a semimetal at van der Waals-like distances, a wide gap semiconductor at covalentlike distances, and in between it displays metallic behavior.

• Received 24 September 2007

DOI:https://doi.org/10.1103/PhysRevB.77.045403