Quantum Monte Carlo Calculation of the Binding Energy of Bilayer Graphene

Abstract

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) meV/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.PACS numbers: 61.48. Gh, 71.15.Nc, 02.70.Ss van der Waals (vdW) interactions play a crucial role in a wide range of physical and biological phenomena, from the binding of rare-gas solids to the folding of proteins. Significant efforts are therefore being made to develop computational methods that predict vdW contributions to energies of adhesion, particularly for materials such as multilayer graphene. This task has proved to be challenging, however, because vdW interactions are caused by nonlocal electron correlation effects. Standard first-principles approaches such as density functional theory (DFT) with local exchange-correlation functionals do not describe vdW interactions accurately. One technique for including vdW interactions in a first-principles framework is to add energies obtained using pairwise interatomic potentials to DFT total energies; this is the so-called DFT-D scheme [1][2][3][4]. The development of vdW density functionals (vdW-DFs) that can describe vdW interactions in a seamless fashion is another promising approach [5][6][7][8]. DFT-based random-phase approximation (RPA) calculations of the correlation energy [9, 10] provide a more sophisticated method for treating vdW interactions; however, RPA atomization energies are typically overestimated by up to 15% for solids [11,12], and hence the accuracy of this approach is unclear. Symmetry-adapted perturbation theory based on DFT allows one to calculate the vdW interactions between molecules and hence, by extrapolation, between nanostructures [13]. Finally, empirical interatomic potentials with r −6 tails may be used to calculate binding energies [14,15], although such potentials give a qualitatively incorrect description of the interaction of metallic or π-bonded two-dimensional (2D) materials at large separation [16].A key test system for methods purporting to describe vdW interactions between low-dimensional materials is bilayer graphene (BLG). Several theoretical studies have used methods based on DFT to calculate the binding energy (BE) of BLG. Some of the results are summarized in Table I, but there is very little consensus. In this work we provide diffusion quantum Monte Carlo (DMC) data for the BE of BLG and the atomization energy of monolayer graphene (MLG), which we have extrapolated to the thermodynamic limit. We find the DMC BE of BLG to be somewhat less than the BEs predicted by DFT-D, although the latter vary significantly from sche...

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