Growth instability in helium films

We study the growth of liquid ${}_{}{}^4{}_{}{}^{}\mathrm{He}$ films on weakly attractive substrates. Close to the substrate the film grows by formation of well defined liquid layers. Above a minimum stable coverage, a liquid monolayer uniformly covers the surface. Upon increasing the coverage a second liquid layer begins to grow by the formation of two-dimensional liquid ‘‘clusters.’’ Above a certain coverage, the second layer leaves vacuum-cluster coexistence, and the system regains the full planar symmetry. The scenario is repeated for a third liquid layer. The results are interpreted in terms of recent experiments of helium on graphite.