Third sound, two-dimensional hydrodynamics, and elementary excitations in very thin helium films

High-precision measurements of third-sound velocity in ${}_{}{}^4{}_{}{}^{}\mathrm{He}$ films with surface densities between 0.16 and 5.25 atomic layers have been taken between 0.1 and 1.5 K. By reformulating Landau's quantum hydrodynamics in two dimensions we have been able to accurately describe these measurements in terms of a surface phonon and surface roton branch of the elementary excitation spectrum. In the thin-film limit surface tension falls to zero and the surface rotons are characterized by an energy gap of 5.3 K.