Quantum Monte Carlo Calculation of the Binding Energy of Bilayer Graphene

We report diffusion quantum Monte Carlo calculations of the interlayer binding energy of bilayer graphene. We find the binding energies of the $AA$-and $AB$-stacked structures at the equilibrium separation to be 11.5(9) and $17.7(9)\mathrm{meV}/\mathrm{atom}$, respectively. The out-of-plane zone-center optical phonon frequency predicted by our binding-energy curve is consistent with available experimental results. As well as assisting the modeling of interactions between graphene layers, our results will facilitate the development of van der Waals exchange-correlation functionals for density functional theory calculations.

Figure 1

Twist-averaged (TA) and non-TA atomization energies of MLG against $N_P^{-5/4}$ as calculated with the DMC method, where $N_P$ is the number of primitive cells in the simulation supercell.

Figure 2

Twist-averaged (TA) BLG BE against $N_P^{-5/4}$ as calculated with the DMC method, where $N_P$ is the number of primitive cells in the simulation supercell. The inset shows non-twist-averaged BEs. The layer separations are the vdW-DF [60] equilibrium values of 3.495 and 3.384 Å for the $AA$-and $AB$-stacked structures, respectively.

Figure 3

BE curve of $AB$-stacked BLG as a function of interlayer distance calculated using DFT, DFT-D, and DMC methods. Our DFT-D calculations used the Tkatchenko-Scheffler (TS) [4], Ortmann-Bechstedt-Schmidt (OBS) [62], and Grimme [63] vdW corrections.