Effects of Substrate Corrugation During Helium Adsorption on Graphene in the Grand Canonical Ensemble

Adsorption of \({}^4\)He 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 utilized a Szalewicz potential for helium–helium interactions and a summation of isotropic interactions between helium and carbon atoms to construct a helium–graphene potential. We implement different levels of approximation 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 layers. We demonstrate that the omission of corrugation within the helium–graphene potential could lead to finite-size effects in both the first and second layers. Thus, a fully corrugated potential should be used when simulating helium in this low-dimensional regime.