Calculation of third-sound velocities for superfluid4He films with3He impurities

The velocities of third sound in superfluid⁴He films containing submonolayer densities of³He are calculated from the variation of film height with the concentration of³He. The present model assumes that the population of the first-excited, transverse, surface state of the³He impurities directly increases the height of the film because these atoms are preferentially found within the film rather than on the surface. The relative populations of the ground-state and the first excited-state are calculated from a many-body, mean-field theory which takes account of the first two transverse branches of the spectra of the states. Intermolecular and one-ripplon exchange interactions are included. Graphs of the variation of third-sound velocity with³He density are given.     

3He Transverse Excited State Occupation in Thin 3He-4He Films

The discovery that ³ He was occupying transverse excited states at submonolayer coverages in ³ He-⁴ He mixture films on a Nuclepore substrate, was a surprise. In this note we discuss the relationship between theory and experiment in attempting to understand the physics of this behavior. We first discuss various single-atom-limit calculations of the level spacing between the ground-state and first excited state. We then introduce a free, quasi-particle picture for analyzing experimental magnetization step data and compare those results with the single-atom-limit calculations. The experiments clearly show excited state occupation at submonolayer coverages in contradistinction with the calculations. We then briefly discuss a microscopic, semi-phenomenological theory which, in agreement with experiment, yields ³ He occupation of the first excited state at submonolayer coverages. The mechanism is a model ³ He-³ He effective interaction due to one ripplon exchange. This effective interaction is density dependent and very long ranged. It strongly modifies the small-k properties of the ³ He self-energy and, in particular, causes the ground-state to first excited state level spacing to decrease with increasing ³ He areal density.     

Recent Progress in Thin 3He–4He Films

We review recent work on the properties of ³He–⁴He thin film mixtures. The subject is introduced by reviewing the contributions made by Gasparini and co-workers. In the first part of this survey, we examine a microscopic calculation of the effects that an adsorbed ³He component has on the collective excitations associated with a ⁴He film, third sound. The work in question computes the change in the third sound velocity due to adding ³He, and we can compare this with existing experiment. For small ³He coverage, the change in the third sound speed depends on the derivatives of the species chemical potentials with respect to the areal density. The microscopic calculation shows oscillations in the third sound speed that reflect the layered structure of the film. In the second part of this survey, we concentrate on the ³He component. An important impact of the ⁴He environment is to change the bare mass in the limit of zero ³He concentration to a hydrodynamic mass. Quasiparticle interactions are introduced through the Landau parameters. Our Landau parameters are determined by fitting s-wave and p-wave T-matrix components using experimental results for the effective mass and the spin susceptibility. We can then predict the thermodynamic behavior of the mixture films at finite polarization, and in addition we can predict the spectrum of zero-sound excitations at all polarizations.     

Path integral monte carlo simulations of thin4He films on a H2 surface

Atomatically thin⁴He films of up to three monolayers on molecular hydrogen (1,1,1) surfaces are studied at T = 0.5 K, using path integral Monte Carlo. We compute the binding energy of⁴He to the H₂ substrate as a function of⁴He coverage and obtain evidence of the prewetting transition. Density profiles perpendicular to the⁴He-H₂ interface are obtained, as well as the zero point motion and effective mass of⁴He parallel to the substrate surface. The superfluid density of⁴He vs. coverage is calculated, and the intermediate scattering function is computed, from which we estimate the speed of third sound. Finally, we calculate the vorticity-vorticity correlation function.     

The velocities of first and second sound in dilute solutions of3He in superfluid4He at very low temperatures

A unified theory of first and second sound in dilute solutions of ³ He in superfluid ⁴ He at very low temperatures is presented. The theory is based on the detailed semimicroscopic model for the ³ He quasiparticle excitations described by Disatnik and Brucker a few years ago. In contrast with Khalatnikov's macroscopic theory, the application of this model enables the derivation of relatively simple expressions for the sound velocities in which no omissions of terms representing contributions due to the thermal expansion are made. The sound velocities are given in the final expressions in terms of various parameters of the ³ He quasiparticle spectrum and effective interaction. These expressions are both highly accurate and easy to use over a wide temperature regime spanning from the quantum limit to temperatures of the order of the ³ He quasiparticle degeneracy temperature. The actual application of the theory to measurements of the sound velocities is described in detail. Numerical values or estimates for various characteristic parameters of the ³ He quasiparticle system, including in particular the ³ He quasiparticle effective mass, are obtained from the comparison between the theory and the experiment. The example of the second sound velocity is used to illustrate a procedure for analyzing data from very low-temperature measurements of the equilibrium properties of the solutions, which is expected to produce meaningful information regarding the parameters of the basic model. In practice, the theory is found to be in a very good accord with the measurements of the sound velocities. The result obtained for the zero concentration limit of the ³ He quasiparticle effective mass (m ₀ =2.19m ₃ ) is somewhat lower than the empirical estimates reported in the past. On the other hand, this result is in very good agreement with variational calculations based on the detailed microscopic theory of the solutions. A discussion of this and other results obtained from the comparison between theory and experiment is included.Work supported in part by the United States-Israel Binational Science Foundation.Killed in action, 16 October 1973.     

3He impurity states on liquid4He: From thin films to the bulk surface

The structure of the states accessible to³He impurities in films of liquid⁴He on Nuclepore is investigated using a density functional approach with a finite-range effective interaction. In thick films, one finds that the two lowest states are localized in the surface region. For thinner films, the variation with film thickness of the first three states results from a delicate balance between the attractive tail of the substrate potential and the quantum finite-size effect. The existence of states localized in the second layer of the films is discussed. The energy difference between the ground state and the first excited state agrees with the recent determination of Higley, Sprague, and Hallock from magnetization measurements. The effective mass of the ground state has a structure similar to that obtained by Krotscheck and coworkers and exhibits a maximum for a⁴He coverage of 0.15 Å^–2, in agreement with the data of Gasparini and coworkers. A similar behavior is predicted for the effective mass of the first, second, and third excited states. The structure of the energy spectrum may also explain former results on third-sound measurements in thin mixture films by Laheurte et al. and by Hallock.Unité de Recherche des Universités Paris 11 et Paris 6 associée au CNRS.     

The Phase of Submonolayer 4He Films Near Monolayer Completion

We study the state of ⁴He films physisorbed to general Lennard–Jones type substrates at coverages near monolayer completion as a function of the range C₃ and well-depth D of the substrate-helium potential. By examining the liquid-state energetics as well as the coverage dependence of the third sound speed and roton energies in the two-parameter space (C₃,D), we can estimate the position of the boundary between those strongly interacting substrates wherein the ⁴He film essentially forms a quasi two-dimensional solid prior to second layer formation and weaker interacting substrates for which the ⁴He film remains mobile and superfluid. Our approach utilizes a combination of information from both variational calculations and also correlated basis function theory to examine in detail the excitation structure in the monolayer liquid as a function of film coverage and substrate potential.      

Possible Phase Transition at Low mK Temperatures in Liquid Helium Mixture Films Adsorbed on Graphite

We report heat capacity and magnetisation measurements of ³He adsorbed on the surface of graphite plated with three atomic layers of ⁴He. For ³He coverages n ₃>4 nm^?2 the heat capacity corresponds to a 2D Fermi fluid. The inferred hydrodynamic mass of the ³He quasiparticles is 1.38±0.05 m₃. The ³He effective mass ratio increases with coverage to 2.4 at n ₃=4 nm^?2, due to Fermi liquid interactions. The heat capacity isotherm exhibits a steplike increase centred on n ₃=4.5 nm^?2, similar to that previously observed on four layers of ⁴He. This is associated with the population of the first excited Andreev surface bound state. However, in the present case, as n ₃ is increased through the step a pronounced anomalous feature develops in the temperature dependence of the heat capacity, around 10 mK. Below 5 mK the heat capacity is approximately linear in temperature. With n ₃=7 nm^?2, we find that this behaviour is very sensitive to small changes in the ⁴He third layer coverage, around the completed third layer. Measurements of the ³He magnetisation,, by continuous wave NMR methods, find a significant increase with decreasing temperature below around 20 mK. Together the data suggest that a phase transition takes place in the film at low mK temperatures.     

The Two-Dimensional World of 3He in 3He-4He Mixture Films

For thin films of ⁴ He at low temperatures the addition of sub-monolayer numbers of ³ He atoms results in the ³ He residing in a ground state at the free surface of the ⁴ He film. For low ³ He coverage the ³ He are a nearly ideal two-dimensional Fermi system. With increasing numbers of ³ He atoms the interactions among the ³ He increase. The results from a number of experiments that reveal the remarkable properties of this rich, interacting, two-dimensional ³ He system are described. These results include the magnetization, the energetics of the ³ He atoms in quantum states, the diffusion of the ³ He along the ⁴ He film, and the ³ He effective mass. The techniques employed include NMR, specific heat, quartz crystal microbalance and third sound. A clearer picture of the properties of the ³ He is now emerging, and preliminary numbers for the ³ He coverage dependence of the Fermi Liquid parameters are presented. Prospects for the observation of superfluidity of the ³ He in this system are discussed.     

Superfluidity of4He films adsorbed on hydrogen plated graphite

The superfluidity of⁴He on graphite with various preplatings of HD is under investigation using a torsional oscillator. Results for a bilayer of HD follow a similar pattern to those obtained earlier on pure⁴He films and are consistent with third sound measurements on graphite plated with a bilayer of hydrogen. In our case the first⁴He layer solidifies, consistent with behaviour observed in NMR studies of³He on a similarly prepared substrate. At a coverage of 11nm^–2 there is the onset of a region in which the transition temperature increases rapidly with coverage and the transition itself becomes sharper. At certain coverages pronounced signatures have been observed in the period shift and dissipation, which may indicate a further phase transition in the film at lower temperatures.     

Properties of 3He in thin 4He films

Substantial progress has been made in our understanding of the properties of ³He atoms in thin films of ⁴He. For such films the ³He occupies discrete quantum states in the film and the system is both rich and complex. Here we discuss progress in this field from several points of view; we briefly discuss early heat capacity and third sound results and concentrate on more recent NMR measurements of the magnetization and relaxation times T ₁ and T ₂. Further experimental work and theory for systems of finite ³He coverage is needed to fully understand this fascinating system.Presenter at the Elba Summer School; authors are listed alphabetically.     

Superfluid Phase Transition of 3He-4He Mixture Films Adsorbed on Alumina Powder

The superfluid phase transition of ³ He- ⁴ He mixture films adsorbed on 500 Å alumina powder has been studied for mixture films whose superfluid thickness is less than a monolayer. The transitions are found to be controlled by the Kosterlitz-Thouless critical line, but a strong broadening of the transition is observed as the ³ He concentration is increased. Analyzing the broadening in terms of a KT vortex-pair theory modified for the the finite powder size yields a vortex core parameter which increases nearly linearly with added ³ He. Also observed in these measurements is a temperature-dependent and ³ He-dependent depletion of the superfluid density at low temperatures, which is thought to arise from the high-frequency ripplon/third sound excitations of the film.     

Quantum-Damping and Nonlinear Ultrasonic Excitations in 3He

Novel attenuation effects and the generation of the third harmonic frequency in nonlinear zero and first sound in ³ He were found in pulsed sound-transmission experiments at various pressures (0, 10 bar), frequencies (10-50 MHz), sound-pulse energies (0.01-110 nJ) and temperatures ranging from 0.8 mK to 200 mK. The nonlinear damping of zero sound increases with the square of the frequency and demonstrates that quantum-damping exists in a Fermi liquid even for low frequency phonons at temperatures as high as 1 mK due to multiple phonon absorption processes. The origin of the additional damping found in first sound at high temperatures and sound pulse powers is unclear, but part of the apparent attenuation is caused by third harmonic generation which was also found in superfluid ³ He-B. In zero- as well as in first sound the third harmonic generation takes place in the leading edge of the propagating sound pulse at times when the fundamental frequency has not even developed to its full amplitude.     

Temperature dependence of the sound velocities and elastic constants of bcc3He

High-resolution measurements of the sound velocity in 20 crystals of bcc³He at constant molar volume (24.1 cm³/mole) show a monotonic decrease of about 0.1% for longitudinal and 0.3% for transverse velocities for a temperature increase from 0.123 to 0.800 K, the change being approximately proportional toT ⁴. A low-lying transverse mode of 102 m/sec was observed for the first time. The orientation of three samples could be inferred from their absolute velocity, and the temperature dependence of all three elastic constants was calculated. The change in adiabatic bulk modulus is in good agreement with the Mie-Grüneisen equation of state. No effect from the exchange interaction on the velocities could be observed.This work was supported by the National Science Foundation.     

Supersaturation and Nucleation in Superfluid 3He–4He Solutions under Elevated Pressures

Nucleation and phase separation kinetics of superfluid ³ He– ⁴ He solutions at various pressures and concentrations were investigated. The measurements of the first sound velocity and the attenuation as well as the liquid dielectric constant determination were used. The study was performed at a constant temperature and pressure and the phase transition was initiated by continuous increasing the ³ He concentration. It is shown that the pressure dependence of the attainable supersaturations is non-monotonic when passing through a maximum at pressure of about 0.1 Bar. The comparison has discovered great differences between the results obtained and theoretical predictions.     

A Third Sound Resonator with Cesium Boundaries

We have created a two dimensional third sound resonator with cesium boundaries on a PMMA-coated glass substrate. At chemical potential values below those necessary for pre-wetting, the cesium boundaries act as non-wet edges, effectively confining the helium to the region enclosed by the cesium. Aluminum transition-edge bolometers and silver electrodes are used as detectors and thermal sources of third sound, respectively. A first-generation resonator is described and preliminary results of third sound attenuation and ⁴ He - Cs reflection coefficient measurements made in the resonator are presented.     

Supercurrents and hydrodynamic modes in3He-A 1 in an electric field

We consider the supercurrent in superfluid³He in an electric field. The possibility to generate hydrodynamic modes (first and second sound) in theA ₁-phase by an oscillating, electric field is proposed. It is shown that the resonance technique can amplify the small amplitude of the second-sound wave. The possibility of measurement is also discussed.     

Transverse waves in superfluid3He-B

We examine the theory of collisionless transverse current waves in bulk superfluid³He-B, including the coupling to the order parameter collective modes. At low frequencies, Ω ≪ δ(T), the order parameter modes do not contribute to the restoring force for a transverse current, and the quasiparticle contribution drops rapidly as the gap in the spectrum develops. Thus, low-frequency transverse sound becomes overdamped at temperatures nearT _c . However, at low temperatures (T ≲0.3T _c ) the off-resonant coupling to the J = 2⁻,M = +-1 modes stabilizes a propagating transverse current mode, with a large phase velocity and low damping for frequencies above a critical frequency that is approximately that of theJ = 2 ⁻ mode. We also discuss the similarities and differences of longitudinal and transverse sound in the superfluid phases. For example, in zero field, right- and left-circularly polarized waves are degenerate. A magnetic field, with , lifts this degeneracy, giving rise to the analog of circular dichroism and birefringence of electromagnetic waves. Thus, transverse waves may be more easily detected in the B-phase than in normal³He.     

Experiments to search for a substrate state for3he adjacent to surfaces in3He-4He mixtures

We describe three experiments designed to search for the bound state for³He adjacent to a substrate which has been predicted by Treiner and co-workers. In each case a bulk³He-⁴He solution is in contact with the substrate of interest. For a Nuclepore substrate, NMR techniques are used to establish that there is no 2D behavior for the³He in the cell; thus, no substrate state is present. For a cesium or hydrogen substrate the technique involves the measurement of the velocity of ordinary sound in the bulk solution as a function of temperature. The cesium and hydrogen experiments are incomplete.     

The Nonwetting Behavior of Dilute 3He-4He Mixtures on Cs

We present evidence for ³ He interfacial bound states at the Cs-liquid He interface and show their influence on the interfacial free energies and the nonwetting behaviour of dilute ³ He- ⁴ He mixtures on Cs. The bound state energy and effective mass for the ³ He atoms at this interface are determined and found to be in good agreement with theoretical predictions. From the temperature dependence of the contact angle, direct evidence for a first order wetting transition at the lower wetting temperature is found. A detailed model is presented for the Cs-He mixture interface free energy and the contact angle and this model is shown to be in excellent agreement with the measurements. There is a short discussion on hysteresis and the thin film state. Finally it is emphasised that the large measured contact angles are only consistent with ³ He bound states together with ripplons at the Cs-He mixture interface