Quantum films adsorbed on graphite: Third and fourth helium layers

Using a path-integral Monte Carlo method for simulating superfluid quantum films, we investigate helium layers adsorbed on a substrate consisting of graphite plus two solid helium layers. The solid helium layers are modeled first as inert, with paths frozen at equilibrated positions, and then as active, with second-layer atoms included in the Monte Carlo updating. In both cases, we observe the formation of as many as three well defined additional layers above the first two and determine the layer promotion density by calculating the density profile and through a calculation of the chemical potential. For liquid layers adsorbed onto the inert solids, we find self-bound liquid phases in both the third and fourth layers and determine the equilibrium density. In the third layer at coverages below equilibrium, we find liquid droplets and a metastable uniform liquid phase and determine the spinodal point that separates these regions. The above phases and their coverage ranges are in good agreement with several experiments. The superfluid density as a function of coverage is also calculated and it is observed to change only weakly around the promotion density. For coverages above the beginning of fourth-layer promotion, we observe continued increase in the third-layer density. We note that the third-layer density increase is perhaps enough to cause solidification in this layer, which would explain heat-capacity peaks observed experimentally for fourth layer coverages and would provide a simple explanation for the plateaus seen in the superfluid coverage. For helium adsorbed on an active second layer, we observe that a self-bound liquid phase occurs in the third layer and we determine the equilibrium density and spinodal point, which remain in agreement with experiment. We find that promotion to both the third and fourth layers is signaled by a change in the density dependence of the chemical potential. We further observe the increase in the second-layer density with increasing total coverage. The coverage dependence of the superfluid density is calculated and a pronounced drop is seen at high third-layer coverages as has also been observed experimentally