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.     

Ultra-Low Temperature Magnetic Properties of Liquid 3He Films

We report measurements of the nuclear magnetization of submonolayer liquid ³ He films adsorbed on a graphite substrate (Papyex) preplated by a monolayer of ⁴ He. In the submilliKelvin temperature range we observe a substantial enhancement of the nuclear magnetization with respect to the degenerate Fermi Liquid value. The unusual temperature dependence of this new contribution to the liquid ³ He film magnetization agrees well with that expected from the theory of weak disorder in two-dimensional (2D) correlated Fermion systems. The effects of disorder and reduced dimensionality suppress the superfluid transition at least to below 180 K.     

Superfluidity in thin4He films: Comparison of onset on particular crystal facets and on disordered substrates

Superfluid flow in unsaturated⁴He films on highly ordered pyrolytic graphite, (001) cleaved MgO, epitaxial gold on mica, polycrystalline gold, and glass has been studied by the heat transport technique. Using a criterion for onset suggested by the Kosterlitz-Thouless theory, we confirm that the locus of onset in the variablesT andp/p ₀ is substrate independent within experimental error, whereas the film thickness at onset varies widely with substrate. The reason for this is not understood. Several aspects of the Kosterlitz-Thouless theory are verified: On polycrystalline gold the film flow impedance decreases approaching the transition from the normal side, consistent with the dependence calculated by Ambegaokar et al. On the superfluid side of onset, power law relations are found between temperature gradient and current, in agreement with the prediction based on thermal dissociation of vortex pairs in the velocity field. The exponents are consistent with the expected variation of the renormalized superfluid density with coverage, including a Nelson-Kosterlitz jump smeared by finite-velocity effects. On MgO we obtain only an upper limit for the film coverage at onset; its consistency with the Nelson-Kosterlitz jump depends on the interpretation of neutron scattering data.Supported in part by NSF grant DMR 78-22697.     

Study of a Helium Film in 10 μm Porous Glass by Torsional Oscillator in Free Decay Mode

Dissipation and superfluid density of a thin helium film (superfluid transition at temperature T_c=0.88 K), placed in 10 m porous glass are studied as a function of oscillation amplitude or AC amplitude at fixed temperatures near superfluid transition. The measurements are performed using a high-Q torsional oscillator in the free decay mode as well as constant drive mode. Results show decreasing superfluid density with increasing velocity and non-monotonic behavior of the dissipation in the film.     

3He film flow on a round rim beaker

The superfluid properties of thin (100–150 nm) of³He were investigated by measuring the rate at which a beaker of liquid³He emptied itself through the adsorbed film, with the film thickness decreasing as the level dropped. A beaker rim with a semicircular cross-section was used to provide a well defined geometry and to avoid the effects of small scratches that may have affected earlier experiments. The film thicknesses were determined by Atkins' oscillaton measurements of⁴He films on the same surface. The superfluid transition temperature in the filmT _c ^F was suppressed below the bulk valueT _c ^B , and was close to being described by 2/(T _c ^F ) = , as expected for A-phase. The critical current density was more than an order of magnitude smaller than expected for pair-breaking. When a⁴He monolayer was adsorbed on the substrate, there was no suppresson ofT _c ^F .     

Digital circularly polarized heterodyne ellipsometer

In this research, a digital circularly polarized heterodyne ellipsometer (DCPHE) is developed, which has a heterodyne interferometer based on a dual-frequency paired circularly polarized laser beam integrated with a digital storage oscilloscope. DCPHE is an amplitude-sensitive ellipsometer that is applicable to real time and precise measurement of ellipsometric parameters. The systematic errors are likewise derived and analyzed. When the incident angle α are set at 60° and 70° in DCPHE, an accuracy of less than 0.7% of the ellipsometric parameter measurement of the SiO₂ thin film deposited on silicon substrate is achieved.     

Torsional Oscillator Experiments with High Stability and Reproducibility

We report experiments of the torsional oscillator to observe the superfluid transition in ⁴ He films in porous glass (the pore diameter is 1m). Stability and reproducibility of the oscillator, which quite often is problematic in previous experiments, is essential for a quantitative analysis of observations in different conditions. It follows that the friction of the superfluid films and the energy dissipation of the solid films are derived from comparisons of measurements for different film thickness.     

Imaging the edge of a 4He prewetting film on a cesium metal surface

The edge of a metastable ⁴ He prewetting film on a cesium metal surface is investigated using polarization interference microscopy. This technique images the local gradient of the coverage through its optical thickness. The cesium metal is a film evaporated on a polished copper substrate. A liquid helium film is deposited on the surface through raising and lowering the bulk liquid surface. Its edge is clearly observed for temperatures below 1.6 K. The apparent optical thicknesses of the films, larger than what is expected for a normal saturated film, remain to be explained.     

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.     

Wetting studies of liquid 4He on various Cs surfaces

Cesium is a surface not wetted by liquid ⁴ He below a certain temperature, T _w 2K. However, one observes that a thick helium film remains on the Cs substrate even if the surface is cooled below T _w from the wetted state. This leaves the question how the system will finally evolve from this metastable state to the thermodynamic equilibrium, represented by a microscopically thin film. We investigate the dynamic and static behavioar of dewetting ⁴ He films on cesiated surfaces. Space and time resolved measurements of the thickness of the helium film are performed using a surface plasmon microscope. We have measured the work function of pure and oxidized Cs via photo current spectroscopy.     

A–BTransition of Superfluid 3He with a Film Geometry

We have performedcwNMR experiments on superfluid ³ He confined to a parallel-plate geometry with a m scale spacing for a wide pressure range. A static field was applied parallel or perpendicular to the plate surface. The spectra of two absorption signals, a main and a satellite, have been observed below the superfluid transition temperature in a parallel field. As the temperature decreased, the main signal decreased with shifts to higher frequencies, and the satellite grew with shifts to much higher frequencies. From the temperature dependence of these signals and the result in the perpendicular field, it is confirmed that the main signal and the satellite correspond to the A phase signal (ABM state) and the B phase signal (BW state), respectively. The temperature dependence of the two signals indicates that a phase transition from the A phase to the B phase occurs with decreasing temperature. By analyzing these signals, we determine A–B transition temperatures experimentaly. TheA–Btransition temperature normalized by the superfluid transition temperature is 0.95 at 20 bar, and decreased further to 0.70 at 0 bar for a thickness of 0.88 m for pure ³ He. The values of T_AB/T_C were slightly elevated when covering the surface with 4.5 layers of ⁴ He film, which suggests that this transition is also influenced by the surface condition.     

Substrate Dependence of the Superfluid Onset of 4He Films

We have performed torsional oscillator measurements of ⁴ He films adsorbed on porous gold and gold preplated with Ar, Ne, D ₂ , HD, and H ₂ . On all substrates, the superfluid response is similar. The thickness of the nonsuperfluid layer as function of the substrate, however, increases monotonically with the well depth of the atom-substrate interaction potential.     

Toward the josephson effect in superfluid helium: How to make 20 nm holes in a 10 nm thick membrane

It was found by electron microscope study that 20 nm diameter holes can be formed in a 10 nm thick self-supported nitrocellulose membrane covered on one side with an island gold film if exposed to the nuclear fragments from a radioactive source. The process of hole formation is a kind of Coulomb explosion. Due to its large atomic number, gold plays a role of an effective source of secondary electrons. However, if the gold thickness is increased, the higher electrical conductivity of the gold film prevents hole formation. This work was initiated in relation to the problem of the Josephson effect in superfluid helium. Our estimates show that there should be a measurable coherent effect for⁴He flow through our membrane with many holes for a temperature close to T, when the coherence length is of order of the hole dimensions.     

Superfluid Transition of 4He for Two-Dimensional Crossover, Heat Capacity, and Finite-Size Scaling

We report heat capacity measurements of confined films of ⁴ He. These studies were undertaken to test predictions of correlation-length scaling. They are the first measurements for completely confined films over a range of confinements, and represent a geometry where criticality changes from 3-dimensions (3D) to 2D. The finite system is realized with a ⁴ He film confined between two, 2 diameter, silicon wafers, which are separated by a small gap. A new technique was developed to bond these wafers at a uniform separation. The gap size, which determines the film thickness, ranges from 0.05 to 0.7 m in the present work, and has better than 1% uniformity. The bonded cells are used to conduct high precision heat capacity measurements using a modified ac technique. This involves oscillating the sample temperature, as in conventional ac calorimetry, but with simultaneous dc regulation of the average temperature. The data are analyzed using a modified Sullivan–Seidel equation, which takes into account in an empirical way the finite conductivity of the cell. This procedure yields heat capacity data with good absolute accuracy and high resolution. Scaling analysis of the data both above and below the bulk transition temperature shows collapse onto universal curves determined only by the ratio of the correlation length to the confinement size. This is true everywhere except near the heat capacity maximum. Here, and into the superfluid side there is lack of scaling which might be associated with 2D crossover. We compare this result with calculations of scaling functions and find that these tend to underestimate the effect of confinement. Comparison with earlier results for cylindrical confinement shows differences which are most striking in the region of the specific heat maximum. The cylindrical and planar confinement data follow similar trends above the superfluid transition of bulk helium. Below the transition, however, the present data show much more structure. Fits of the scaled planar data above the transition to an empirical scaling function yield a correlation length exponent of _eff=0.674±0.001.     

Specific Heat and Superfluid Density of 4He near T λ of a 33.6 nm Film Formed Between Si Wafers

We report measurements of superfluid density and specific heat of a 33.6 nm film near the superfluid transition. The film is formed between two patterned and directly bonded silicon wafers. These measurements were undertaken with the primary purpose of understanding coupling and proximity effects in a situation when the film was in contact with helium in a larger confinement (Perron et al. in Nat. Phys. 6:499, 2010; Perron and Gasparini in Phys. Rev. Lett. 109:035302, 2012). However, these data are also relevant to issues of correlation-length finite-size scaling. This is the thinnest hard-wall confined film for which such scaling has been tested for the specific heat and superfluid density. One expects that at some small thickness such scaling should fail. We compare our results with previous data of helium in a similar confinement but at larger thickness. We find good agreement with scaling in regions where previous data scaled, and confirm the lack of scaling where previously reported. In our analysis we consider a native oxide growth between the etching and bonding steps of cell fabrication and its effect on our scaling analysis.     

Optical interferometry in superfluid3He-B

We report interferometric measurements on 0.1 ... 1 mm thick films of superfluid ³He-B. The menisci of three different rotational states of the superfluid were observed and analyzed theoretically using two-fluid hydrodynamics: These are (i) the equilibrium vortex state in which the superfluid and the normal components corotate (solid body rotation), (ii) the vortex-free state (the Landau state), in which only the normal component rotates, and (iii) the quasistationary vortex state in which only the superfluid fraction rotates (pure superfluid rotation). The Landau state manifested itself by a reduced parabolic meniscus at rotation speeds below the critical angular velocity 0.2 rad/s for vortex formation. Transition from the Landau state to the equilibrium vortex state yielded a sudden deepening of the meniscus when _c was exceeded. After a rapid halt of the cryostat, we observed a novel meniscus which was produced by the superfluid rotation while the normal component was at rest. The enhanced depth of this meniscus is governed by the reactive mutual friction parameter B'.By employing laser light, both for imaging and for thermomechanical excitation, we measured the response of a thin superfluid layer to a heat pulse and analyzed it within the theory of two-fluid hydrodynamics. The data were employed, using the dispersion relation for thin film oscillations, to deduce the second viscosity coefficient ₃ close to T_c.     

Low Temperature Heat-Capacities of Liquid 3He Thin Films

We have measured the heat capacity of ³ He thin films adsorbed on graphite at an areal density of 15.0 nm ^–2 down to as low as 100 K. The second-layer ³ He behaves as a degenerate 2D Fermi fluid in the whole temperature range we studied. We observed no anomalous behavior in the heat capacity near 3 mK in contradiction to the recent report by other workers. This indicates that possible superfluid transitions would be below 100 K. Instead, a small and temperature-independent contribution to the heat capacity was observed, which we attribute to nuclear-spin degrees of freedom in glassy solid ³ He trapped in substrate heterogeneities.     

Scaling of the superfluid density in superfluid films

We study scaling of the superfluid density with respect to the film thickness by simulating the x — y model on films of size L × L × H (L H) using the cluster Monte Carlo. While periodic boundary conditions where used in the planar (L) directions, Dirichlet boundary conditions where used along the film thickness. We find that our results can be scaled on a universal curve by introducing an effective thickness. In the limit of large H our scaling relations reduce to the conventional scaling forms. Using the same idea we find scaling in the experimental results using the same value of v = 0.6705.We wish to thank F. M. Gasparini for providing us with his data of the superfluid density for films of various thickness and for clarifying discussions. This work was supported by the National Aeronautics and Space Administration under grant no. NAG3-1841.     

Superfluid flow dissipation in two dimensions

A model is presented describing the onset of nonlinear dissipation in two-dimensional helium films for allT _KT, whereT _KT is the Kosterlitz-Thouless transition temperature. The superfluid velocity is included in the renormalization equations of Kosterlitz and Thousless, and it is shown that the model predicts a characteristic velocity for a given temperature, film thickness, and frequency where onset occurs. No critical velocity is predicted except atT=0. The model neglects the effects of prinning, and preliminary measurements seem to substantiate this assumption.     

Dissipation by pinned vortex lines in the superfluid helium film

The status of theoretical and experimental work on dissipation in the helium film is reviewed, and it is concluded that there does not yet exist a satisfactory theoretical interpretation of dissipation in the film which can account for the complete range of observed phenomena below the superfluid transition temperature T. Although the most recent theory, which accounts for dissipation in terms of intrinsic fluctuations in the flow, has been successful in a temperature interval just below T, attempts to extend the theory to include all temperatures below T have not met with the same degree of success. A new model is proposed which accounts for dissipation in superfluid helium film transport in terms of the continuous generation of pinned vortex lines. In principle, this model is similar to one advanced by Vinen, involving the growth and decay of a tangled array of vortex lines. Qualitatively, it is shown that the present mechanism can account for many of the phenomena observed in helium film transport experiments at temperatures well below the transition. For example, sharp changes in the flow rate are associated with changes in the number of pinned vortex lines. In addition, the theory predicts that at superfluid stream velocitiesv _sthat just barely exceed the critical velocityv _c0for the appearance of dissipation, the rate of dissipation Q is given by Q=AN(v_s–v_c0)^3/2 whereN is the number of pinned vortex lines, andA is a constant determined by the vortex line parameters. The value of 3/2 for the exponent is a clear prediction of the theory, and it represents the first precise, numerical prediction by any theory of a physical quantity which is associated with dissipation in the helium film, and which can be measured experimentally.The research for this paper was supported by the Defence Research Board of Canada, Grant number 9550-57.