Strong covalent bonding between two graphene layers

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 $0.156\phantom{\rule{0.3em}{0ex}}\mathrm{nm}$. Simultaneously, C--C in-plane bonds are considerably weakened from partial double bond $(0.141\phantom{\rule{0.3em}{0ex}}\mathrm{nm})$ to single bond $(0.154\phantom{\rule{0.3em}{0ex}}\mathrm{nm})$. This polymorphic form of graphene bilayer is metastable with an activation energy of $0.16\phantom{\rule{0.3em}{0ex}}\mathrm{eV}∕\text{cell}$ with respect to the standard configuration bound by van der Waals forces at a larger separation between planes $(0.335\phantom{\rule{0.3em}{0ex}}\mathrm{nm})$. Carbon atoms form four single bonds in a geometry mixing 90\ifmmode^\circ\else\textdegree\fi{} and 120\ifmmode^\circ\else\textdegree\fi{} 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 $9\phantom{\rule{0.3em}{0ex}}\mathrm{GPa}$, 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.