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An uncertainty in studying twisted bilayer graphene (TBG) is the minimumenergy geometry, which strongly affects the electronic structure. The minimumenergy geometry is determined by the potential energy surface, which isdominated by van der Waals (vdW) interactions. In this work, large-scalediffusion quantum Monte Carlo (QMC) simulations are performed to evaluate theenergy of bilayer graphene at various interlayer distances for four stackingregistries. An accurate registry-dependent potential is fit to the QMC data andis used to describe interlayer interactions in the geometry of near-magic-angleTBG. The band structure for the optimized geometry is evaluated using theaccurate local-environment tight-binding model. We find that compared to QMC,DFT-based vdW interactions can result in errors in the corrugation magnitude bya factor of 2 or more near the magic angle. The error in corrugation thenpropagates to the flat bands in twisted bilayer graphene, where the error incorrugation can affect the bandwidth by about 30\% and can change the natureand degeneracy of the flat bands.

Registry-dependent potential energy and lattice corrugation of twisted bilayer graphene from quantum Monte Carlo