Path integral Monte Carlo simulations of thin4He films on a H2 surface

The adsorption of ⁴ He films for coverages from1/4 to3 monolayers ona H₂ surface at low temperatures is studied with Path Integral Monte Carlo. We calculate the binding energy per ⁴ He atom to the substrate, density profiles of ⁴ He and H₂, zero point motion of ⁴ He and H₂, and the superfluid density of ⁴ He.     

4He Atoms Incident on a Superfluid 4He Slab: Quantum Sticking, Scattering and Transmission

We present the results of a microscopic theory of the scattering, transmission, and sticking of ⁴ He atoms impinging on a zero temperature ⁴ He slab at near normal incidence. The theory includes coupling between different modes and allows for inelastic processes. The present work focuses on the elastic reflection and transmission of a ⁴ He atom in the sense that we examine these intensities for atoms which have the same energy as the incident atoms. We find a considerable loss of total intensity due to scattering into multiple excitations. The reflected signal is in qualitative and semi-quantitative agreement with experimental results for ⁴ He atoms scattered from the surface of bulk helium. The transmission intensity — which has not been measured — shows a very strong energy dependence. Moreover, we show that this dependence is substantially different from the Feynman level theory, which doesn't permit the decay of the single excitation into multiple excitations, and thus cannot describe a reduction in total intensity. In our theory, the major source of decay of elastic transmission and reflection (i.e., sticking) is from the production of ripplons at the liquid-vacuum interfaces.     

4He in Nano-porous Media: Superfluidity and Quantum Phase Transition

This paper reviews recent findings of novel phenomena in ⁴He confined to a nano-porous glass. We examined pressure–temperature (P-T) phase diagram of ⁴He confined in a porous Gelsil glass that had nanopores 2.5 nm in diameter, by torsional oscillator and pressure studies. The obtained phase diagram is fairly unprecedented the superfluid transition temperature approaches zero at 3.4 MPa, and a novel nonsuperfluid phase exists between the superfluid and solid phase. These observations indicate that the confined ⁴He undergoes a superfluid-nonsuperfluid-solid quantum phase transition at zero temperature. We propose that the nonsuperfluid phase may be a localized Bose-condensed state in which global phase coherence is destroyed by a strong correlation between the ⁴He atoms or by a random potential. ⁴He in nanospace is an excellent model system for studying a strongly correlated Bose liquid and solid in a confinement potential.     

Density functional calculations for the structure of vortices in superfluid4He

The structure of a rectilinear vortex in superfluid ⁴ He at zero temperature is studied using a Density Functional method. The superfluid circulation is included via the Feynman-Onsager approximation. The energy and the density profile of a vortex are predicted for several values of the external pressure. The instability of the vortex line at negative pressure is discussed.     

Phase transitions in the growth of4He films

Using a microscopic, variational approach we examine the growth of⁴He absorbed to graphite and alkali substrates. We find that superfluid layers are formed and their behavior as a function of coverage is closely related to the one of a purely two-dimensional superfluid. The growth of a new layer undergoes a phase transition from a cluster formation into the connected superfluid when the coverage is increased. Based on the important connection to the two-dimensional fluid we propose a microscopic theory of quantum vortices in⁴He films at zero temperature, in which single vortices are treated as quasiparticles. We calculate the energy needed to create the single vortex, vortex inertial mass, microscopic interaction between vortices and binding energy of the vortex-antivortex pair as a function of density. We predict that at the⁴He superfluid density less than about 0.037 Å^–2 the binding energy of the pair becomes negative, indicating a phase transition into a new state where vortex-antivortex pairs are spontaneously created.     

Adsorption of3He and4He on copper and on argon-coated copper below 20 K

Measurements have been made of adsorption isotherms of ³ He and of ⁴ He on copper and on a monolayer of argon deposited on copper in the temperature range 6.18–18.55 K and in the pressure range 0.25 to 75 Torr. From these many isotherms, calculations have been made of the isosteric heat of adsorptionQ _st/R. In the limit of zero coverage on the argon monolayerQ _st/R=76±2 K for ³ He and 76±2 K for ⁴ He. For adsorption on the bare copper,Q _st/R is difficult to extrapolate to zero coverage, but it probably lies (for both ³ He and ⁴ He) between 135 and 165 K. At theoretical monolayer helium coverage,Q _st/R=44±2 K for ³ He on the argon monolayer and 47±2 K for ⁴ He. At theoretical monolayer helium coverage on the bare copper,Q _st/R=61±4 K for ³ He and 77±5 K for ⁴ He. The results are compared with theoretical evaluations for helium adsorbed on an argon monolayer and with some previous experimental data, and the agreement is found to be fair. All the data are summarized in tables. Finally, a review is given of evaluations, including those from this work, of the monolayer capacity of ³ He and ⁴ He on the substrates studied.Work supported by a contract with the Department of Defense (Themis Program) and with the Office of Naval Research and by a Grant from the National Science Foundation.     

The Effective Mass and Binding Energy of 4He in 3He in the Fermi Liquid Region

We have measured the solubility of ⁴ He in liquid ³ He down to about 40 mK and at pressures from zero up to 24 atm. The solubility was obtained from the thickness of the superfluid film in contact with unsaturated solutions of ⁴ He in ³ He as a function of temperature. By fitting the solubility data to Fermi liquid theory, we obtained the parameters m ₄ ^* and as a function of pressure. Here, m ₄ ^* is the effective mass of ⁴ He in liquid ³ He and the difference in binding energy between ⁴ He in pure ⁴ He and ⁴ He in liquid ³He. This difference has a minimum near 10 atm. The average of the results for m ₄ ^* , at different pressures, is (1.3 ± 0.2)m ₄. This agrees with the many body calculations of de Saavedra et al., and with the Stokes hydrodynamic mass using the partial volume of ⁴ He in ³ He, v ₄ ^* . The partial volume was obtained by taking the derivative of with respect to pressure.     

On Polarization-Induced Zero Temperature Spin Wave Damping in Dilute 3He

We have observed spin waves in dilute ³ He, spin polarized by a ⁴ He circulating dilution refrigerator. The maximum polarization is a factor 5 higher than the equilibrium polarization in the magnetic field of 10.54 T at temperatures between 10 and 20 mK. The measured spin wave damping is about a factor 4 lower than the damping expected from previous spin echo experiments in ³ He- ⁴ He mixtures, which confirmed the prediction of polarization-induced spin wave damping at zero temperature in Fermi liquids. Our experiment shows that the existence of polarization-induced spin wave damping remains an open question.     

Thermodynamics of the liquid-solid interface in dilute solutions of3He in4He

We show that the (p, T, x) phase diagram of⁴He close to melting pressure (25.3 bars) with small concentrations of³He and at very low temperatures has several unanticipated and novel features. For pressures between 25.3 bars and a triple point pressurep*, estimated to be 25.8 bars, we find a dilute liquid solution of³He in equilibrium with solid⁴He. The concentration of the liquidx _c increases from zero to the dilute liquid solubility limitx ₀ as the pressure increases from the pure⁴He melting pressure atT=0 top*. We explore the possibility of self-cooling by lowering the pressure throughp*. We also consider the effects of a strong magnetic field, and show that it lowersx _c. An estimate of the kinetic growth coefficient is given. Finally, we discuss the possible adsorption of³He on the melting front and the consequent faceting enhancement of the solid⁴He.     

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.     

Self Diffusion in Solid 4He and 3He-4He Mixtures Near the bcc-hcp Phase Transition

We report experiments on the plastic flow of solid ⁴ He and ³ He- ⁴ He mixtures of 1.4% and 2.8% near the bcc-hcp transition. Plastic flow was generated by moving a wire through a macroscopic single crystal. We found that the plastic flow rate both in pure ⁴ He and in mixture helium crystals is enhanced in vicinity of the bcc-hcp phase transition. The results are interpreted in terms of self diffusion in the solid. Values of the self diffusion coefficient D_s at the respective transition temperatures of pure ⁴ He and of the mixtures are very close, and reach that found in normal liquids. The activation energy for self diffusion in the mixtures is lower by up to 3 K than in pure ⁴ He. We suggest that similar to what is observed in bcc metals, self-diffusion in solid He takes place through phonon assisted atom-vacancy exchange. The enhancement of the diffusion near the bcc-hcp transition is a result of the softening of a short wavelength transverse phonon. The temperature dependence of the energy of the phonon calculated using our data is in accord with the Landau theory of a phase transition driven by a soft mode. Work hardening was observed in mixture crystals, but not in pure ⁴ He. This implies that ³ He impurities pin dislocation lines.     

Pinning of Dislocation Motion in bcc Solid 3He

We have measured the dissipation of dislocation motion in bcc solid ³ He using the high-Q torsional oscillator technique at 1079 Hz. We observed a broad maximum in the temperature dependence of the dissipation. The maximum of the dissipation can be explained by the theory of Granato and Lucke in which the dislocation mobility depends upon the interactions of dislocations with point defects. ⁴ He impurities tend to bind to the dislocation lines at low temperatures and pin this dislocation motion. The maximum of the dissipation corresponds to the depinning of the dislocation motion. From the amplitude dependence of the depinning temperature we first obtained the activation energy of 1.03 K of the impurity ⁴ He atom trapped on the dislocations in bcc solid ³ He at a molar volume of 24.30 cm ³ /mol. The activation energy of the impurity atom in bcc ³ He was found to be larger than the value of 0.7 Kin hcp ⁴ He.     

Ground-State Properties of Two-Dimensional 3He-4He Mixtures: Energetics and Structures

Using a variational Jastrow wavefunction extended to include a three-body correlation function and a hypernetted chain (HNC) and Fermi hypernetted chain (FHNC) scheme with contribution from elementary diagrams, we analyze ground-state energies and structural properties of two-dimensional ³ He- ⁴ He mixtures. The mixtures are in equilibrium at lower density compared to a pure ⁴ He system because of the large zero-point energy and statistical correlations due to the fermionic nature of ³ He. We evaluate the lowering of ground-state energies as a function of the impurity concentration and total density of mixtures. Comparing the results with boson ³ He- ⁴ He mixtures, we evaluate the energy shifts coming from the statistics and analyze the enthalpy to study the miscibility and mobility of each component of the mixture.     

Structure of negative ion in normal liquid 3He

We present a microscopic calculation of the electron-bubble radius and energy in liquid ³He at zero applied pressure. The two-particle distribution function is approximated as input by the radial distribution function of bulk ³He. The theoretical value of the radius at 14 is about 30% below the experimental value obtained from mobility measurements. The model presented here predicts an electron-bubble surface that is less sharp compared to what was obtained by Shih and Woo for the bubble in ⁴He. Around the bubble the matter density profile appears to be characterized by a high-density region which is about one atomic layer in thickness. The density peak at the bubble surface exceeds the bulk density by about 10%. The approximation schemes are discussed and the source of discrepancy with experiment speculated upon.Work supported in part by the National Science Foundation through grant No. DMR 76-18375.     

The solubility of4He in3He below 0.1 K

The Zharkov-Silin Fermi Liquid theory of solutions of⁴He in non-superfluid liquid³He has been applied to the recent phase separation data of Nakamura et al. At zero pressure, the difference in binding between a⁴He atom in liquid⁴He and in liquid³He is smaller than previous estimates, and the⁴He effective mass is close to the bare mass. The volume measurements of Laheurte show that the difference in binding has a minimum near 11 atm. This implies an enhanced solubility of⁴He in³He below 0.1 K at this pressure, although there is experimental evidence that the solubility at 0 K remains zero.     

Observation of Anomalously Low Momentum Transfer in the Low Energy Scattering of Large 4He Droplets From 4He and 3He Atoms

The momentum transferred to large superfluid ⁴ He droplets in low energy ( 4–10 K) scattering from ⁴ He and ³ He atoms was determined from time of flight measurements after the droplets have passed through a low temperature (T = 1.7–4.2 K) scattering box filled with the gas of either He isotope. The results are compared with ³ He droplets scattered from either ⁴ He or ³ He gas for which all of the incident momentum is transferred, as expected for classical capture of the scattering gas atoms. In the case of the ⁴ He droplets a smaller momentum transfer is found amounting to 65% for ⁴ He atoms and 45% for ³ He atoms but only at the lowest collision energies. These results are consistent with transmission of some of the atoms through the droplets.     

Generalized Jastrow variational method for liquid3He-4He mixtures atT=0 K

The ground state energy of a dilute solution of mass-3 fermions in liquid⁴He is analyzed by a variational procedure based on the Jastrow many body theory. The antisymmetry of the wave function for fermions is incorporated following the procedure given by Lado, Inguva, and Smith. A set of coupled integrodifferential equations is solved in the hypernetted chain approximation yielding expressions for the binding energy of³He-⁴He mixtures; the radial distribution function is given together with the total energy for various values of density and the interparticle separationr _s.     

Temperature Increase of Highly-Polarized Fermi Liquids in Spin-Echo Experiments

We show that there are restrictions on the maximum tipping angle that can be used without significantly raising the temperature of the ³ He distribution in high B/T spin-echo experiments with pure liquid ³ He and ³ He- ⁴ He solutions. The temperature increase occurs during the diffusion process as quasiparticles in mixed-spin states are scattered and converted into thermal excitations at the spin-up and spin-down Fermi surfaces. This temperature increase can mimic the effects of zero temperature attenuation, leading to a higher values of the measured anisotropy temperature T_a. We analyze the dependence of the increase on polarization, initial temperature, ³ He concentration, and tip angle, and estimate the size of the effect in recent experiments.     

Acoustical Experiments on Superfluid 3He-4He Mixtures in Aerogel

This report discusses our results on the superfluidity of ³ He- ⁴ He mixtures in a 98% porosity silica aerogel. We have used low frequency sound to probe helium mixtures confined to aerogel, and have observed both the slow mode of superfluid ³ He in aerogel, which is manifested only below T_c, and an additional sound mode present only in the mixture. We attribute this novel sound mode to the slow-mode in the ⁴ He rich phase of the dilute ³ He- ⁴ He mixture. This mode exhibits positive frequency shifts below T_c in aerogel, while above T_c the mode is observed at a temperature independent frequency until close to T where it shifts to zero frequency.     

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