Abstract
We study third sound in thin 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., . In very thin films, this result clearly must be modified to account for the effects of nonuniform film density. Utilizing the variational, hypernetted-chain–Euler-Lagrange theory as applied to inhomogeneous boson systems, we calculate accurate chemical potentials for both the superfluid film and the physisorbed . 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 coverage in the linear (low-concentration) regime, which is then studied for the two substrates as a function of film thickness and compared to existing experiments. density profiles are calculated as a function of 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 et al. [Phys. Rev. Lett. 53, 2421 (1984)]. Our results predict that the addition of a small amount of can increase, as well as decrease, the third-sound speed relative to that of the pure film. Further, we show that the addition of a small amount of can destabilize the film and drive a phase separation into lateral regions of -rich and -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.
- Received 24 March 2005
DOI:https://doi.org/10.1103/PhysRevB.73.134514
©2006 American Physical Society