Solidification ofHe4clusters adsorbed on graphene

Abstract

We determined the ground state of $^{4}\mathrm{He}_{N}$ clusters adsorbed on one side of graphene for selected cluster sizes in the range from $N=20$ to $N=127$. For all investigated clusters variational and diffusion Monte Carlo simulations were performed at $T=0$ K, and in addition for a selected subset finite temperature path integral Monte Carlo. At $T=0$ K the liquid or solid character of each cluster was investigated by restricting the phase using corresponding importance sampling trial-wave functions. The $^{4}\mathrm{He}$-graphene interaction was modeled as a sum of individual $^{4}\mathrm{He}$-C interactions, where both isotropic and anisotropic models were tested; also the effect of the substrate-mediated McLachlan interaction was investigated. We have found homogeneous crystallization in models of anisotropic interactions, starting from clusters with $N=26$ atoms in simulations without the McLachlan interaction, and between $N=37$ and 61 when it is included. The atoms become increasingly delocalized as one moves from the center of the cluster to the perimeter, evidenced by the Lindemann parameter. On the other hand, in the case of the isotropic interaction model, a liquidlike structure is more favorable for all considered cluster sizes. We use a liquid-drop model to extrapolate the energy per particle to the $N\ensuremath{\rightarrow}\ensuremath{\infty}$ limit, and the results are compared with the values obtained in studies of bulk $^{4}\mathrm{He}$ on graphene. Low-temperature path integral Monte Carlo simulations are in agreement with ground-state results.