Corrugation effects on the second ⁴He adsorbed layer on graphene

Adsorption of ⁴He on graphene substrates has been a topic of great interest due to the intriguing effects of graphene corrugation on the manifestation of commensurate solid and exotic phases in low-dimensional systems. In this study we employ worm algorithm quantum Monte Carlo to study helium adsorbed on a graphene substrate to explore corrugation effects in the grand canonical ensemble. We implement different levels of approximation for including two-body interactions between helium and carbon to achieve a smooth potential, three partially corrugated potentials, and a fully ab initio potential to test the effects of corrugation on the first and second layer. Our results demonstrate the role of substrate corrugation during the adsorption process and support the importance of using accurate emph{ab initio} potentials in simulations of the helium-graphene system