Ellipsometry of Liquid Helium Films on Gold, Cesium, and Graphite

We have developed a modulated null ellipsometer with sub-monolayer resolution to measure adsorbed liquid helium thin films at temperatures below 4 K. Adsorption isotherms of ⁴He on gold, cesium, and graphite are presented. For Au and Cs substrates, the reflecting surface for our ellipsometric measurements is the metallic electrode of a quartz crystal microbalance(QCM). Performing both types of measurements simultaneously on the same substrate provides a direct method of converting the ellipsometric signal into an absolute film thickness without constructing a detailed model of the refractive index of the substrate. Isotherms on gold above and below T¸ show that the ellipsometric signal is unaffected by the superfluid transition; the ellipsometer measures the total film thickness independent of the superfluid fraction. Isotherms on cesium above the wetting temperature show a prewetting step. Isotherms on clean graphite show steps due to layering.     

Quartz Crystal Microbalance Study of Superfluid 4He Films on Gold and Porous Gold Surfaces

The superfluid transition in sub-rnonolayer ⁴He films was studied using quartz crystal microbalance (QCM). We recently improved the QCM technique by replacing the conventional gold electrodes with porous gold, thus increasing the surface area and therefore sensitivity by 40 times. Simugtaneous measurements were taken for QCMs with flat and porous gold electrodes contained within the same copper cell. For both QCMs the superfluid transition temperature was found to be proportional to the ⁴He film thickness. The superfluid transition temperature at each film coverage was greater for porous gold than for flat gold electrodes.     

Superfluid Density of 4He Films Adsorbed in Porous MCM-41 Ceramic

No Heading The superfluid transition of ⁴He films adsorbed in MCM-41 ceramic with 40-Â-diameter, micron-length cylindrical channels is studied with a torsion oscillator technique. For film coverages above 1.7 layers a finite-size Kosterlitz-Thouless transition becomes apparent in the data, with considerable broadening of the KT jump of the superfluid fraction. With decreasing helium coverage the extent of the broadening increases, indicating that the vortex core size is increasing. The data is consistent with the Machta-Guyer theory of the KT transition in a cylindrical channel, but with a coverage-dependent vortex core size. At low temperatures a linear decrease of the superfluid fraction with temperature is observed, indicating a zero-dimensional excitation.PACS numbers: 67.40.Db, 67.40.Rp, 67.40.Vs, 67.40.Hf     

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.     

Helium Adsorption on Lithium Substrates

We have developed a cryogenic pulsed laser deposition (PLD) system to deposit lithium films onto a quartz crystal microbalance (QCM) at 4 K. Adsorption isotherms of ⁴He on lithium were measured in the temperature range between 1.42 K and 2.5 K. The isotherms are qualitatively different from isotherms on strong substrates such as gold and weak substrates such as cesium. There is no evidence of the formation of solid-like layers of helium, and the helium coverage is approximately linear in the pressure over a wide range. By measuring the low coverage slope of the isotherms, the binding energy of helium to lithium was found to be approximately −13.6 K. For lithium substrates less than approximately 100 layers thick, the chemical potential at which the superfluid transition was observed was surprisingly sensitive to the details of lithium deposition. This work was supported by NSF grant DMR 0509685.     

4He films on graphite studied by neutron scattering

The properties of ⁴He films adsorbed on graphite have been studied by neutron scattering. In particular excitations of the commensurate phase of the monolayer are discussed. The first two adsorbed layers are solid and the next ones stay liquid. At the boundaries of the superfluid film excitations could be studied. Also the phonons, maxon and rotons of the film are investigated. An explanation of the lower density of the very thin films compared to bulk ⁴He is given.Presented by H. J. Lauter.     

Superfluid Onset and Capillary Condensation

We present experimental results on the superfluid onset of ⁴He adsorbed onto porous gold and evaporated CaF₂ films grown on the electrodes of quartz microbalances (QCM). Adsorption and desorption isotherms were measured on the porous substrates in the range of 1.2 to 2.2 K. The isotherms were used to construct phase diagrams in the μ–T plane showing hysteresis closure points and superfluid onsets. At low coverage, the superfluid onset showed both the abrupt frequency shift and dissipation peak characteristic of a conventional KT transition. Within hysteresis loops, a dissipation peak is observed, but the nearly discontinuous frequency shift is replaced by a smooth and gradual decoupling of the superfluid component as the coverage is increased. The gradual onset of superflow was analyzed using ideas from percolation theory.      

Fluid States of Helium Adsorbed in Nanopores

We have studied helium adsorbed in new nanopores which have regular structures from nano-cage to three-dimensionally (3D) connected pores. Adsorption potential and layer formation of the adsorbed helium are observed by the vapor pressure for the adsorption. New paradigms of zero-D and 1D helium fluids are realized in nano-cages and nano-channels, respectively. The superfluid onsets (transitions) in the 1D and 3D nanopores show obvious dependence on the pore connections. The superfluid in the 3D pores has properties similar to the Bose-Einstein condensation of the 3D Bose atomic gas. The films of the ³He gas formed in the ⁴He preplated nanopores show the dimensional crossover depending on the pore connection: from the 2D Boltzmann gas to a 1D or 3D gas state with decreasing temperature. This gas changes to the degenerate state in each dimension at the lower temperatures. Extremely high frequency measurements of the helium adatoms on flat substrate determined the superfluid vortex parameters of the ⁴He films, and revealed a slippage (decoupling) of the helium adatoms in the non-superfluid state.     

Heat Capacity Measurements of 3He-4He Mixture Films

We report heat capacity measurements from our on-going experiments on two-dimensional liquid ³He on superfluid ⁴He thin films absorbed on Nuclepore. The ³He coverage dependence of the heat capacity for 0.02–0.50 bulk-density layers of ³He with 3.10 bulk-density layers of ⁴He over the temperature range 40≤T≤200 mK is presented. We find the effective mass of ³He on 3.10 layers of ⁴He is greater than that on 4.33 layers of ⁴He, consistent with our previous magnetic susceptibility measurements.     

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.     

Superfluid helium in porous media

The superfluid properties of ⁴He absorbed in porous media are discussed. Emphasis is given to the nature of the superfluid transition for helium contained in a variety of different porous structures. Recent heat capacity and superfluid measurements for helium in Vycor glass and other porous media are presented in some detail. The onset of superfluidity as a function of adsorbed helium coverage at zero temperature, or boson localization, is touched on briefly. The problem of dissipation of superflow in porous media, especially in the vicinity of the superfluid transition, 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.     

3He and 4He Coverage Dependence of FA 0 and FS 1 in Thin Mixture Films

No Heading We report additional heat capacity measurements and analysis from our experiments on two-dimensional liquid. ³He on superfluid ⁴He thin films absorbed on Nuclepore. The ³He heat capacity for sub-monolayer coverages of ³He with 3.10 bulk-density layers of ⁴He for T 40 mK is discussed. We incorporate these measurements with earlier NMR work in similar coverage ranges and deduce preliminary values for the two-dimensional Fermi Liquid parameters for the ³He for 3.10 layers of ⁴He.PACS numbers: 67.60.Fp, 67.65.+z.     

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.     

The solid-liquid surface tension at a helium/cesium interface

The existence of a wetting transition for helium adsorbed on cesium provides an experimental opportunity to investigate the solid-liquid surface tension. We have extracted the temperature dependence of the solid-liquid surface tension at the⁴He/Cs interface from our earlier measurements of the wetting temperature of pure⁴He on thin layers of cesium overlaying gold. More recently we have measured the wetting temperature as a function of the³He concentration for³He-⁴He mixtures. An analysis of these experiments paralleling Andreev's investigation of the free surface reveals³He bound states at the helium/cesium interface.This work was supported by NSF grant DMR-9223775.     

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.     

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.     

Thin Helium Film on a Glass Substrate

We investigate by Monte Carlo simulations the structure, energetics and superfluid properties of thin ⁴He films (up to four layers) on a glass substrate, at low temperature. The first adsorbed layer is found to be solid and “inert”, i.e., atoms are localized and do not participate to quantum exchanges. Additional layers are liquid, with no clear layer separation above the second one. It is found that a single ³He impurity resides on the outmost layer, not significantly further away from the substrate than ⁴He atoms on the same layer.     

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.     

Transverse Sound in Helium Filled Aerogel

Transverse sound in superfluid ⁴He in 92% porous aerogel has been studied in a resonator with thin slab geometry, in the temperature range 0.6 to 2.8 K. The sound velocity and dissipation in the saturated aerogel were modelled using two fluid hydrodynamics, modified to account for the presence of the aerogel. Partially filled aerogel was also studied. Adsorption and desorption isotherms displayed hysteresis. For capillary-condensed films, the tortuosity and the dissipation scale with the amount of helium.