4He clusters adsorbed on graphene

Abstract

We report the results of a study of ${}^{4}$He${}_{N}$ clusters, for $2\ensuremath{\le}N\ensuremath{\le}40$, adsorbed on one and both sides of a graphene sheet. The ground-state properties are determined using variational and diffusion Monte Carlo calculations at zero temperature, and in addition path integral Monte Carlo simulations at finite temperature are performed for some selected cluster sizes. For the interaction of helium atoms with graphene, we compare several models: a smooth He-graphene potential that depends only on the distance to the graphene sheet and potentials constructed as a sum of individual He-C interactions where two possibilities for this He-C interaction are tested. In this way, we assess the effect of corrugation on the binding properties of helium clusters. Furthermore, we study the influence that the graphene-mediated McLachlan dispersion energy has on the He-He interaction. The McLachlan interaction weakens the attraction between helium atoms, which turns out to have a significant effect on the binding energy and the shape of adsorbed ${}^{4}$He clusters. We find that clusters adsorbed on opposite sides of graphene are bound, but according to the He-He pair distribution function across the graphene sheet, pair correlations are very weak. For a large enough number of particles, solidlike $\sqrt{3}\ifmmode\times\else\texttimes\fi{}\sqrt{3}$ structures start to become energetically preferred for the model of anisotropic corrugation without the McLachlan interaction. For the other models, the ground state of the studied clusters is clearly liquidlike.