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.     

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.     

Vortex core size in submonolayer superfluid4He films

The superfluid transition of⁴He films adsorbed on 500 Å diameter slip-cast alumina powder is measured with a torsion oscillator technique for films with transition temperatures between 50 and 700 mK. The transitions are found to be controlled by the universal Kosterlitz- Thouless critical line, but a strong increase in the broadening of the transition is observed for the thinnest films. Analysis in terms of vortex pair excitations shows that this broadening results from a vortex core size that increases rapidly as the film is thinned, scaling roughly with the interparticle spacing of the superfluid submonolayer. Third sound modes are identified in the dissipation, in addition to a broad peak from the vortex unbinding. This system provides evidence of a three-dimensional superfluid transition mediated by vortex excitations.     

Slippage of 4He Films Adsorbed on Grafoil

We applied the quartz-crystal microbalance (QCM) technique to ⁴He films adsorbed on grafoil. It was found that both of nonsuperfluid ⁴He films and the inert layers underneath the superfluid film slip under a certain condition at low temperatures, and that the temperature at which these films start to slip depends on the ⁴He areal density. In addition, this slippage also depended strongly on the amplitude of the quartz crystal.     

On the Existence of Supersolid 4He Monolayer Films

Extensive Monte Carlo simulations of ⁴He monolayer films adsorbed on weak substrates have been carried out, aimed at ascertaining the possible occurrence of a quasi-two-dimensional supersolid phase. Only crystalline films not registered with underlying substrates are considered. Numerical results yield strong evidence that ⁴He will not form a supersolid film on any substrate strong enough to stabilize a crystalline layer. On weaker substrates, continuous growth of a liquid film takes place.     

Effect of 3He on Third Sound Attenuation in Thick 4He Films

We have performed measurements of third sound attenuation in thick films of superfluid ⁴He in the presence of small amounts of ³He. The attenuation due to ³He appears to depend linearly on the number density of ³He atoms in the film. We discuss the results in context of a recently proposed mechanism where the attenuation is caused by the interaction of the excitations in helium with the trapped vortices.     

Phase Diagram of 4He Film in 3D Nanopores of ZTC

In the study to examine effects of three-dimensional (3D) film connectivity on superfluid ⁴He film in the pore network, we have measured heat capacities of ⁴He film adsorbed in zeolite templated carbon (ZTC), which is an assembly of graphene fragments and has network of 1.2 nm pore with the 3D period of 1.4 nm, shorter than those of nanoporous materials studied so far. From the heat of desorption, the ⁴He film adsorbed in ZTC was observed to be formed up to about 1.4 atomic layers. Heat capacities of the ⁴He film are rather similar to those on SiO₂-based porous materials than those on graphite, except for large heat capacities of monolayer ⁴He film. At low coverages, the heat capacity rapidly decreases below a temperature T _L, suggesting a localized state of ⁴He at T<T _L. The T _L almost monotonically lowers with increasing the coverage. Heat capacity isotherms show maxima around 1.1 layers, which suggests quantum degenerate fluid (Bose fluid) above the coverage. From these results, the phase diagram of ⁴He film adsorbed in ZTC has been determined.     

Interfacial Friction of 3He Films Adsorbed on Grafoil

We measured the interfacial friction of ³He films adsorbed on Grafoil (exfoliated graphite) using the quartz-crystal microbalance (QCM) technique, and compare present results with those of ⁴He films. In the same manner as ⁴He films, the friction decreases below a certain temperature T _S , and T _S depends on the areal density of ³He film. In two-atom and three-atom thick films, however, T _S of ³He films is lower than that of ⁴He films. Furthermore, the decrease in the friction still remains above five-atom thick films of ³He while it disappears in four-atom thick films of ⁴He and the superfluid onset is manifest.     

Nuclear magnetic susceptibility of3He adsorbed on graphite below 4.2 K

The nuclear magnetic susceptibility of³He films adsorbed on graphite substrates was measured by means of pulsed NMR techniques at 10 and 20 MHz. Submonolayer, monolayer, and multilayer coverages were examined, as well as one monolayer of³He mixed with various amounts of⁴He. The temperature range of measurements extended from 0.35 to 4.2 K. For pure³He and for³He mixed with⁴He the nuclear magnetic susceptibility displays departures from Curie's law. The observed behavior in pure³He layers can be fitted to an ideal-Fermi-gas curve with an effective degeneracy temperature of 0.15 K. The nuclear magnetic susceptibility of³He–⁴He films is also found to fall below the values predicted by Curie's law as the temperature is lowered, but the results suggest that in this case the film is not uniform, possibly as a result of a phase separation in the film at low temperatures.Work supported in part by the National Science Foundation and a Navy Equipment Loan contract.     

Heat Capacity of Dilute 3He–4He Films on Graphite

The heat capacity of dilute ³He–⁴He films is measured to clarify whether the second adsorbed layer of ⁴He films on graphite solidify into the so-called “4/7 phase.” The ³He areal density is fixed at 0.2 nm^?2, whereas the ⁴He areal density is gradually increased. The measured heat capacities suddenly decrease with an increasing areal density approaching that of the 4/7 phase. Above the areal density of the 4/7 phase, the heat capacities do not reduce completely to zero and have finite values. The behavior of the heat capacity does not change over a rather wide areal density regime, although it suddenly increases or recovers at around the areal density of the third-layer promotion. These behaviors can be interpreted as the separation of ³He–⁴He mixture films into a ³He-rich phase and a ⁴He-rich phase, with the ³He-rich phase solidifying into the 4/7 phase and the ⁴He-rich phase remaining fluid below the areal density of the third-layer promotion. These observations strongly suggest that a ⁴He film adsorbed on a graphite surface does not solidify into the 4/7 phase.     

Preliminary Measurement of the Critical Casimir Effect near the Tricritical Point in 3He–4He Mixture Films

We report a preliminary measurement of the critical Casimir effect in ³ He- ⁴ He mixture films near the tricritical point. Whereas we had found that the pure ⁴ He film adsorbed on Cu substrates thins due to the critical Casimir force near the lambda transition, in our present experiments we find that the adsorbed mixture film thickens near the tricritical point. This difference in behavior most likely reflects the difference in the universality class of these two phase transitions and the difference in boundary conditions that the order parameter must satisfy at liquid-substrate and liquid-vapor interfaces.     

Ellipsometric Study of Superfluid Onset in Thin Liquid 4Helium Films

We have developed a modulated null ellipsometer capable of measuring single layers of adsorbed ⁴He films at 1.4 K. The small optical index of liquid helium, the extreme sensitivity to temperature gradients, and the requirement of sub-monolayer stability over many hours presents significant experimental challenges, which will be briefly discussed. The main goal of our experiments is to independently measure the superfluid and normal coverage in thin adsorbed ⁴He films. This is a particularly important issue for helium films on intermediate strength substrates such as rubidium and thin cesium, where previous measurements indicate that prewetting and the Kosterlitz-Thouless transition interact strongly, and the K-T transition appears to have nonuniversal features. Independent determination of the superfluid and normal fraction can be accomplished by using the ellipsometer in conjunction with a quartz crystal micro balance (QCM). QCM measurements rely on viscous coupling of the fluid layers, and therefore respond only to the normal component of a ⁴He film. In contrast, the ellipsometer is sensitive to the total thickness, independent of the state (superfluid or normal) of the film. By combining the QCM and ellipsometric measurements we can determine the total coverage, the normal fluid component and thus the superfluid fraction.     

Heat capacities of Ar,Ne,4He-Ar,and4He-Ne films adsorbed on Cu at low temperatures

Heat capacities of Ar and Ne monolayers adsorbed on Cu are measurable at 1–4 K. Temperature dependences are similar to the low-temperature law for harmonic oscillators, but the empirical characteristic temperatures of 11–15 K are much lower than can correspond to independent adatoms oscillating in substrate sites. The magnitudes and temperature dependences do not match those predicted for surface modes of an absorbent coated with inert impurities or for the collective modes of epitaxial films. A model involving the excitations in non-epitaxial films appears to offer an explanation of the observed magnitudes and temperature dependences. The heat capacities of⁴He adsorbed on preplated Ar or Ne show little variation with the number of Ar layers, or between Ar and Ne coatings.Research supported by The National Science Foundation.     

Nonlinear excitations in a film of a mixture of 3He and superfluid 4He

Using a combination of the superfluid ⁴He film model of Rutledge et al. and the layered model of Guyer and Miller we have investigated the nonlinear excitations in a film of a mixture of ³He and superfluid ⁴He. We have shown that such a system allows one-dimensional soliton excitations. These solitons, however, are not stable with respect to transverse perturbations. In that case the system allows two-dimensional lump solutions.The paper was presented at Stat. Phys. 18, IUPAP International Conference on Statistical Physics held at Berlin, August 1992.     

Heat diffusion in normal4He and3He thin films

We report measurements of heat diffusion at the surface of a glass substrate coated by normal⁴He and³He thin films. As the normal Helium film is grown, we observe for both isotopes that the diffusion of heat is strongly altered. Clearly a new diffusive channel is associated to the presence of the normal film itself, and for an³He film thickness of 7a.l. two distinct characteristic diffusion times are measured. The shorter time is characteristic of the diffusion of heat in the bare substrate while the longer one is associated to the diffusive process taking place in the normal adsorbed film. Considering the two diffusive channels as independent, we are able to obtain the diffusive contribution of the normal He film. The analysis of these data leads us to propose the picture of phonons traveling in the film with a wavevector parallel to the substrate plane. The existence of this independent diffusive mode, with a characteristic time larger than that of the substrate, is supported by the very slow decrease at long times of the measured temperature deviation for the coated substrate.     

Observation of 4He Superfluidity in 1.8 nm-Pores

No Heading Superfluid properties of ⁴He adsorbed in uniform straight pore 1.8 nm in diameter were studied using a torsional oscillator. In the pore, the first one or two layers of adsorbed. ⁴He are solid, therefore the pore diameter is effectively reduced to about 1.1 or 0.4 nm. In order to investigate whether ⁴He becomes superfluid in such a narrow pore, we performed the oscillator experiments for two cases: ⁴He is adsorbed (1) on the bare substrate and (2) on the pore completely filled with N₂ atoms. In the latter case, only superfluid film coating the surface of the substrate grain can be detected. Compared with this case, an additional superfluid signal originating from ⁴He in the pore is observed for the bare substrate. This strongly suggests that ⁴He in the pore is superfluid.PACS numbers: 67.40.–w, 67.70.+n     

4He Fluid in Extremely Narrow 1D Channels 1.5?nm in?Diameter

To examine whether one-dimensional (1D) helium quantum fluid is realized in narrower channels than those studied previously, we have measured heat capacities of ⁴He adsorbed in nanoporous material FSM with straight 1D channels 1.5 nm in diameter. From the heat of desorption for adsorbed ⁴He, the coverage n _f, up to which ⁴He film grows in the channels, is determined to be 15.4 ??mol/m² using the Frenkel-Halsey-Hill model. At coverages sufficiently below n _f, the temperature dependence of the ⁴He heat capacity has a shoulder, above which adsorbed ⁴He is delocalized from the substrate. On the other hand, the depression of the heat capacity indicating quantum effects has not been observed up to n _f, which suggests that ⁴He film in the channels remains amorphous-like normal fluid. Just above n _f, the quantum effect is observed in ⁴He adatoms on the grain surface of FSM powder, which indicates that 1.5 nm channels are slightly below the limit required to realize quantum effect in the inside ⁴He fluid.     

Observation of Zero-Sound at Atomic Wave-Vectors in a Monolayer of Liquid 3He

The elementary excitations of a strongly interacting two-dimensional Fermi liquid have been investigated by inelastic neutron scattering in an experimental model system: a monolayer of liquid ³He adsorbed on graphite preplated by a monolayer of solid ⁴He. We observed for the first time the particle-hole excitations characterizing the Fermi liquid state of two-dimensional liquid ³He, and we were also able to identify the highly interesting zero-sound collective mode above a particle-hole band. Contrarily to bulk ³He, at low wave-vectors this mode lies very close to the particle-hole band. At intermediate wave-vectors, the collective mode enters the particle-hole band, where it is strongly broadened by Landau damping. At high wave-vectors, where the Landau theory is not applicable, the zero-sound collective mode reappears beyond the particle-hole band as a well defined excitation, with a dispersion relation quite similar to that of superfluid ⁴He. This spectacular effect is observed for the first time in a Fermi liquid (including plasmon excitations in electronic systems).     

Dynamical Response of Liquid 3He Films Adsorbed on Solid Substrates

Within the general framework of linear response theory, we investigate the excitation spectrum of ³He films adsorbed on substrates. Starting from the quasiparticle spectrum and the effective interaction derived in a finite range density functional scheme, we analyze the properties of the particle-hole (ph) excitations as well as the collective modes in the Random Phase Approximation. On the one hand, the most important features of the ph spectrum, originated in the band structure of the single particle spectrum together with the fermionic character of the quasiparticles, are clearly exhibited when the free response to a probe parallel or transverse to the film is considered. On the other hand, for any film, the collective spectrum presents various branches which, in many situations, can be associated with predominantly intraband longitudinal transitions or with almost pure interband transitions. Analyzing the RPA response of a monolayer on substrates of very different adsorbing power (cesium and graphite) we can interpret the nature of the existing collective excitations and determine the influence of the geometrical features of the film on the effective quasiparticle interaction responsible of these oscillations.