van der Waals screening by graphenelike monolayers

The ubiquitous van der Waals (vdW) interaction determines the fundamental properties of material surfaces. Here, we show that graphene can partly screen the vdW energy by up to 53%, as tested in a graphene trilayer and a sandwiched BN/graphene/BN multilayer using the random phase approximation and density functional theory based many-body-dispersion method. The vdW screening turns weaker in semiconducting and insulating graphenelike monoatomic layers, displaying a strong correlation with the band gap and the dielectric constant of materials, but depends less on the screened materials. The revealed relationship between the vdW screening and the fundamental electronic structure of the graphenelike material will be instrumental in the rational control of surface interactions.