Third sound and stability of thin He3 - He4 films

We study third sound in thin He3 - He4 mixture films from first-principles, microscopic theory and compare these results to the usual film-averaged, hydrodynamic approach. The hydrodynamic approach yields third-sound speeds that depend only on the thickness of the superfluid film and the distribution of impurities-i.e., He3. In very thin films, this result clearly must be modified to account for the effects of nonuniform He4 film density. Utilizing the variational, hypernetted-chain-Euler-Lagrange theory as applied to inhomogeneous boson systems, we calculate accurate chemical potentials for both the He4 superfluid film and the physisorbed He3. 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. We are thus able to gauge the range of applicability of the film-averaged hydrodynamic results as applied to thin quantum liquid films. We study third sound on two model substrates: Nuclepore and glass. We compute the change in third-sound speed as a function of He3 coverage in the linear (low-concentration) regime, which is then studied for the two substrates as a function of He4 film thickness and compared to existing experiments. He3 density profiles are calculated as a function of He4 film thickness, and we show explicitly the smooth transition from Andreev states in the thick-film limit to lateral mixtures in the submonolayer limit. This effect was first seen by Noiray [Phys. Rev. Lett. 53, 2421 (1984)]. Our results predict that the addition of a small amount of He3 can increase, as well as decrease, the third-sound speed relative to that of the pure He4 film. Further, we show that the addition of a small amount of He3 can destabilize the film and drive a phase separation into lateral regions of He3 -rich and He3 -poor patches. This latter result may help explain the phase transitions reported by Bhattacharyya and Gasparini [Phys. Rev. Lett. 49, 919 (1982)] and Csáthy, Kim, and Chan [Phys. Rev. Lett. 88, 045301 (2002)] in thin mixture films.