Structure of boson quantum films

We employ a quantitative microscopic theory of nonuniform quantum liquids to explore the structure and growth of thin films of ${}_{}{}^4{}_{}{}^{}\mathrm{He}$ adsorbed to a substrate. Particular emphasis is placed on answering the question of how ‘‘two dimensional’’ an atomic monolayer is in a realistic physical situation. An optimized variational ansatz for the wave function employing pair and triplet correlations provides a quantitatively accurate description of the zero-temperature ground state of the many-particle system. In both the two- and three-dimensional bulk${\mathrm{-}}^4$He limits, our predicted energetics are in excellent agreement with the equation of state obtained (in two dimensions) from Monte Carlo calculations and (in three dimensions) from experiments. For an adsorbate monolayer we find a binding energy slightly below that of two-dimensional ${}_{}{}^4{}_{}{}^{}\mathrm{He}$. When more atoms are added to the system, the quantum-liquid film grows through a sequence of at least three phase transitions separating layered homogeneous phases from nonuniform surface-coverage phases. By investigating the corresponding energetics and distribution functions we elucidate the important properties of these quantum-film structures as well as quantify the departure of the monolayer from the purely two-dimensional system.