Stacking-dependent binding energy of bilayer graphene from diffusion Monte Carlo*

The phase diagram of twisted bilayer graphene as described by the electronic properties is sensitive to geometry relaxations, the determination of which requires an accurate description of the van der Waals interaction between bilayers. However, there does not exist enough accurate data to fully parameterize the registry dependence between the bilayers. We use the accurate [PRL 115 115501 (2015)] diffusion Monte Carlo (DMC) to parameterize the interaction between layers of graphene. The large DMC data set of 36 energy evaluations as a function of registry is used to refit the Kolmogorov–Crespi potential [PRB 71 235415 (2005)]. The new parameterization results in larger grain boundaries between regions of AB stacked graphene in the moiré lattice. We will discuss the effects of this difference in atomic structure on the electronic structure of bilayer graphene.