The phase of submonolayer ⁴He films near monolayer completion

We study the state of ⁴He films physisorbed to general Lennard-Jones type substrates at coverages near monolayer completion as a function of the range C₃ and well-depth D of the substrate-helium potential. By examining the liquid-state energetics as well as the coverage dependence of the third sound speed and roton energies in the two-parameter space (C₃,D), we can estimate the position of the boundary between those strongly interacting substrates wherein the ⁴He film essentially forms a quasi two-dimensional solid prior to second layer formation and weaker interacting substrates for which the ⁴He film remains mobile and superfluid. Our approach utilizes a combination of information from both variational calculations and also correlated basis function theory to examine in detail the excitation structure in the monolayer liquid as a function of film coverage and substrate potential.