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

TL;DR

This paper uses quantum Monte Carlo simulations to accurately determine the potential energy surface of twisted bilayer graphene, revealing significant errors in density functional theory predictions that impact electronic properties.

Contribution

It introduces a registry-dependent potential fitted to QMC data for modeling interlayer interactions in twisted bilayer graphene, improving accuracy over DFT-based methods.

Findings

QMC provides more accurate interlayer potential energies.

DFT-based vdW interactions can significantly underestimate corrugation.

Errors in corrugation affect flat band bandwidth and degeneracy.

Abstract

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