Path-integral Monte Carlo studies of helium on graphite

A path integral Monte Carlo method for simulating quantum films has been developed and applied to helium adsorbed on graphite. We find that the helium film grows in a series of atomically thin layers, each possessing several two-dimensional phases. The first three layers have been studied in detail. Our simulation of the first layer has been performed both with and without substrate corrugations. When corrugations are neglected, liquid and solid phases occur. We determine the low temperature equations of state and find coverage ranges for the liquid and solid phases and their coexistence regions. The second layer promotion density is also found. When substrate corrugations are included, we find that, in order of increasing density, the following experimentally observed first layer phases form: a $3\times 3$ commensurate solid, a domain wall solid, and an incommensurate solid. For densities below the commensurate coverage, we find direct evidence that the monolayer consists of commensurate solid patches coexisting with a low density vapor, which clarifies conflicting experimental interpretations of this region. In the second layer, we find the following uniform phases, in order of increasing coverage: a superfluid liquid phase, a $7\times 7$ commensurate solid phase, and an incommensurate solid phase. The coverage ranges for each of these phases and the coexistence regions that separate them are determined. From these ranges we deduce a low temperature phase diagram and demonstrate that the growth of the commensurate solid phase causes the experimentally observed disruption of superfluidity. Properties for each of the uniform phases are determined, and the third layer promotion density is found. For the third and fourth layers, self-bound superfluid phases are found, and neither layer solidifies. In the third layer, we determine coverage ranges for the gas-liquid and metastable liquid phases that occur below the equilibrium density. We further observe second layer compression by the higher layers and suppression of superfluidity in the third layer. The fourth layer promotion density is determined. All phases found in our simulation, their coverage ranges, calculated specific heats, and the layer promotion densities are in agreement with experimental results.