Thin Helium Films Research Articles

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.

Study of the Superfluid Transition in Two-DimensionalHe4Films

We have studied the superfluid transition of a thin two-dimensional helium film adsorbed on an oscillating substrate. The superfluid mass and dissipation when analyzed in terms of the dynamic theory of Ambegaokar, Halperin, Nelson, and Siggia support the Kosterlitz-Thouless picture of the phase transition in a two-dimensional superfluid. The value for the jump in the superfluid density at the transition given by Kosterlitz and Thouless, ${\ensuremath{\rho}}_{s}({{T}_{c}}^{\ensuremath{-}})=8\ensuremath{\pi}{k}_{\mathrm{B}}{(\frac{m}{h})}^{2}{T}_{c}$, is in good agreement with estimates from experiment.

High‐precision phase‐velocity measurements utilizing a continuous‐wave feedback technique

A common technique for measuring the phase velocity of an acoustic wave under free‐field conditions has been a determination of the phase shift between transmitted and received signals. We report here a modification of this scheme involving the addition of a feedback loop which increases the precision of the absolute velocity measurement. In addition, this technique provides automatic tracking of relative velocity variations with high precision and noise immunity. Measurements illustrating this technique for acoustic waves in thin superfluid helium films are presented with precisions of better than 80 ppm obtained.

Onset of superflow in thin helium films

The two-dimensional $\mathrm{XY}$ model is applied to superfluid onset in thin $^{4}\mathrm{He}$ films. The spins of the system belong to droplets of bulk liquid that form on films thicker than the critical coverage, and the interactions are due to Josephson tunneling between droplets. A simple law describes the variation of onset temperature with coverage measured in calorimetric and mass-transport studies on Grafoil.

Time delay of phonon pulses in thin helium films

Phonons backscattered from surfaces covered by thin helium films were found to be time delayed if detectors sensitive to thermal frequencies were used. With a sample geometry which excluded diffusive reflection we determined a quantitative measure of the delay.

Inhomogeneities in thin helium films

We report a study of the inhomogeneities in thin helium films due to the van der Waals potential by a resonant acoustical technique. The van der Waals constant between helium and quartz is estimated to be α=65±5 K (layer)3; the model leads to a solid helium layer on the substrate of the order ofH=2.2a 0 . A comparison is made with data extracted from interferometric acoustical methods and third-sound type experiments.

Modified equation of state for thin 4He films

A modified equation of state for thin films of superfluid helium is used to analyze experimental results on third sound propagation. The combined effects of this modification and a consideration of fluctuation phenomena serve to improve markedly the comparison between theory and experiment.

Bose-Einstein condensation in a two-dimensional system at constant pressure

Using techniques developed by Greenspoon and Pathria, a rigorous, asymptotic analysis of the onset of Bose-Einstein condensation in a finite two-dimensional system at constant pressure is carried out. Some of the results obtained by Imry, Bergman, and Gunther, who first considered this problem, are upheld while others get modified. In particular, a macroscopic occupation of the single-particle ground state at finite temperatures is indeed possible. As the critical region, $T\ensuremath{\simeq}{T}_{c}$, is approached from above, the volume of the system becomes subextensive, ${V}_{c}=O(\frac{N}{\mathrm{ln}N})$, which is both necessary and sufficient for the onset of Bose-Einstein condensation in the system. For instance, if the system is now cooled even at constant volume $V(={V}_{c})$, the condensate fraction gradually builds up and becomes nonnegligible as $T$ approaches ${T}_{0}\ensuremath{\simeq}\frac{({T}_{c})}{2}$; below ${T}_{0}$, it grows steadily as $(1\ensuremath{-}\frac{T}{{T}_{0}})$. On the other hand, if we continued to cool the system at constant $P$ its volume, over a thermodynamically negligible range of temperatures, would reduce to values $O({N}^{\frac{1}{2}})$ which, in turn, would be accompanied by an abrupt accumulation of practically all the particles of the system into the single-particle ground state ${\ensuremath{\epsilon}}_{0}$. The specific heat ${C}_{P}$, after having passed through a maximum, would also finally reduce to subextensive values. Phase transitions of this kind may be of relevance to the physical behavior of thin helium films and helium submonolayers.

Electron localization on a liquid-helium surface

A theoretical treatment is given of the localization or self-trapping of the motion of electrons bound in extrinsic surface states on liquid helium. For a thin helium film (\ensuremath{\sim} 100 \AA{}) on a substrate we find a trapping energy of about 8 K. We investigate the breakdown of very thin films and show that in the bulk case an earlier estimate of the trapping energy by Shikin must be revised.

Ideal adsorbed multilayer thin films: some thermodynamic implications

With a proper choice of coordinates and for certain substances over a limited temperature range, the information contained in a whole family of adsorption isotherms coalesces into a single universal curve. Such behaviour can be related to a particularly simple thermodynamic model. This model and some of its implications are explored in detail. In particular, thermodynamic internal self-consistency demands that there be a unique (generally non-linear) relationship between the mass adsorbed and the film thickness which is completely deducible from measured adsorption isotherms plus bulk thermodynamic data. It is independent of assumptions regarding the form of the van der Waals attraction binding the adsorbate to the adsorbent substrate. The integral equation embodying this relationship is derived and exhibited. As an example of its use the equation is applied to the case of thin films of helium II.

Is the onset of superfluidity connected to "connectivity"?

As their explanation for the relatively precipitous onset of superfluidity in thin helium films which we have reported, Dash and Herb have recently advanced their connectivity theory. An analysis of this theory is presented here and some predictions are deduced from it. These predictions appear to be in contradiction to the experimental facts. Hence, the theory seems inapplicable to the onset phenomena reported.

Free Surface of a Rotating HeII Film

Stimulated by recent conflicting experimental results, we have investigated the properties of quantized vortex lines in thin films of superfluid helium. The shape of the liquid–vapor interface in the presence of a single line is calculated. The depression of the interface ("dimple") that results is considerably smaller for the film than for the bulk liquid. The critical rotational frequency for the appearance of the first vortex line is only slightly reduced below the bulk value.

Onset of Superfluidity in Thin Films of Liquid Helium

Onset of Superfluidity in Thin Films of Liquid Helium

Comments on the article: ‘The two-fluid model of the helium film’

It is argued that the thermodynamic approach used by Goodstein and Saffman in their theory of thin superfluid helium films is incorrect. Their theory does not explain Keller’s experiment. The value they obtained for the convection velocity of third sound in a film with superfluid flow is consequently unfounded theoretically. Their calculation of third sound attenuation is shown to be incomplete.

Phonon Interference in Thin Helium Films Using Superconducting Tunnel Junctions

Phonon Interference in Thin Helium Films Using Superconducting Tunnel Junctions

Macroscopic Quantum Uncertainty Principle and Superfluid Hydrodynamics

By application of a macroscopic quantum uncertainty principle to the flow of superfluid helium, one can understand the onset of third sound in thin helium films, and the large excess absorption of third sound in thick helium films.

Theory of helium submonolayers. II. Bandwidths and correlation effects

Continuing our earlier efforts to develop a microscopic theory for physically adsorbed helium submonolayers, we address ourselves to a number of questions raised at the 1970 Symposium on Thin Helium Films and present here results of model calculations. In particular, we compare heats of adsorption and bandwidths calculated for helium adsorbed on different surfaces of fcc argon, and compute the correlation energy (or lateral heat of vaporization) per adsorbed atom.

Topical issue on thin helium films

Topical issue on thin helium films

Hydrodynamics and third sound in thin superfluid helium films

The linearized hydrodynamic equations for thin superfluid films, which were developed by the author and solved previously by an analytical approximation, 1 have now been solved numerically to yield the velocity and attenuation of thirdsound waves. The numerical solution covers a much wider range of film thicknesses and third-sound frequencies than was accessible by the analytical approximation. The numerical results coincide with the analytical approximation over the range where the latter was expected to be valid, i.e., for very thin films and low frequencies. Outside that region the striking deviations are in the attenuation coefficient ~, which is plotted in Fig. 1 as a function of film thickness at T = 1.3°K

Third-sound resonance and thermal resistance in unsaturated helium films

We have obtained a thermodynamic state of thin helium films which permits precision measurements of their properties. Third-sound resonances indicate a transition in the superfluid density of these films. This transition is accompanied by an exponential rise in the thermal resistance of the helium film which indicates the formation of high-energy excitations of 0.08 eV. The dissipation at resonance indicates that thermodynamic fluctuations are the principal mode of third-sound damping.