Third sound and stability of ³He-⁴He mixture films

We study third sound and the interaction between ³He adatoms in two thin ³He-⁴He mixture films from a first-principles, microscopic theory. Utilizing the variational, hypernetted-chain Euler-Lagrange (HNC-EL) theory as applied to inhomogeneous boson systems, we calculate chemical potentials for both the ⁴He superfluid film and the physisorbed ³He. Numerical density derivatives of the chemical potentials lead to the sought-after third sound speeds that clearly reflect a layered structure of at least seven oscillations. In this paper, we report third sound on model substrates: Nuclepore, and sodium. We find that the effect of the ³He depends sensitively on the particular ⁴He film coverage. Our most important result is that, with the addition of ³He, the third sound speed can either increase or decrease. In fact, in some regimes, the added ³He destabilizes the film and can drive "layering transitions", leading to fairly complicated geometric structures of the film in which the outermost layer is predicted to consist of phase-separated regions of ³He and ⁴He.