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Previous measurements of the superfluid density ${\ensuremath{\rho}}_{s}$ and specific heat for $^{4}\mathrm{He}$ have identified effects that are manifest at distances much larger than the correlation length ${\ensuremath{\xi}}_{3\text{D}}$ [Perron et al., Nat. Phys. 6, 499 (2010); Perron and Gasparini, Phys. Rev. Lett. 109, 035302 (2012); Perron et al., Phys. Rev. B 87, 094507 (2013)]. We report here measurements of the superfluid density which are designed to explore this phenomenon further. We determine the superfluid fraction ${\ensuremath{\rho}}_{s}/\ensuremath{\rho}$ from the resonance of 34-nm films of varying widths $4\ensuremath{\le}W\ensuremath{\le}100\phantom{\rule{0.28em}{0ex}}\ensuremath{\mu}\text{m}$. The films are formed across a Corbino ring separating two chambers where a thicker 268-nm film is formed. This arrangement is realized using lithography and direct Si-wafer bonding. We identify two effects in the behavior of ${\ensuremath{\rho}}_{s}/\ensuremath{\rho}$: one is hydrodynamic, for which we present an analysis, and the other is a correlation-length effect which manifests as a shift in the transition temperature ${T}_{c}$ relative to that of a uniform 34-nm film uninfluenced by proximity effects. We find that one can collapse both ${\ensuremath{\rho}}_{s}/\ensuremath{\rho}$ and the quality factor of the resonance onto universal curves by shifting ${T}_{c}$ as $\mathrm{\ensuremath{\Delta}}{T}_{c}\ensuremath{\sim}{W}^{\ensuremath{-}\ensuremath{\nu}}$. This scaling is a surprising result on two counts: it involves a very large length scale $W$ relative to the magnitude of ${\ensuremath{\xi}}_{3\text{D}}$ and the dependence on $W$ is not what is expected from correlation-length finite-size scaling which would predict $\mathrm{\ensuremath{\Delta}}{T}_{c}\ensuremath{\sim}{W}^{\ensuremath{-}1/\ensuremath{\nu}}$.

We report measurements of the superfluid fraction rho(s)/rho of films of (3)He-(4)He mixtures confined between silicon wafers at 0.0483 microm separation. The data obtained using adiabatic fountain resonance (AFR) can be used to test for the first time expectations of correlation-length scaling in the case of planar mixtures. For the mixtures, the data for rho(s)/rho collapse well on a universal function. The dissipation associated with AFR can also be scaled, and indicates two-dimensional crossover. These results are in contrast to pure (4)He, where over a wider range of confinements, the data for rho(s)/rho are found not to scale.

We report measurements of the specific heat of thick helium films to test scaling predictions near the superfluid transition, Tl. These films, bounded by two silicon wafers, range in thickness from 0.107 to 0.692 mm. The specific heat of the films is suppressed relative to that of bulk helium, and the difference of the data from bulk helium scales well with the exponent of the correlation length. We propose an empirical scaling function which fits the data well for T . Tl, and yields the surface specific heat. We also compare the data with various theoretical calculations and experiments. We find that the calculations underestimate the effect of confinement. [S0031-9007(97)02843-3] The motivation for this work was to study effects of confinement on the heat capacity of liquid 4 He near the superfluid transition temperature, Tl. Compared to bulk helium, the heat capacity of a finite sample is suppressed, and the maximum is rounded and shifted below Tl. The magnitude of these effects depends on the confinement size L, boundary conditions, and, if appropriate, the lower crossover dimension of the confined system.

Proximity and coupling effects between contiguous regions of 4He are expected to occur over a distance on the order of the temperature-dependent correlation length ξ (t). We present recent measurements of 4He confined in arrays of (2 μm)3 boxes linked through a 4He film. The specific heat and superfluid fraction of the 4He in these geometries reveal effects which occur at distances much larger than expected. These effects include enhancements in specific heat and superfluid fraction as well as shifts in the temperatures of the superfluid onset and specific-heat maximum. Our analysis gives evidence for the relevance of the finite-size correlation length ξ (t,L) in explaining these effects even though the effects occur at distances over an order of magnitude larger than ξ (t,L). These results can be used to deduce the finite-size scaling locus for ξ (t,L). The spatial distance over which coupling and proximity effects are observed raises questions regarding the physical mechanism for these effects and the interpretation of ξ (t). Lastly, these results are discussed in connection to other measurements of 4He in confined geometries, and the relevance to other critical systems.

Measurements of the heat capacity in two-dimensional helium-3 adsorbed on graphite provide further evidence of an unexpected liquid state at temperatures near absolute zero.

We report measurements of the superfluid fraction ${\ensuremath{\rho}}_{s}/\ensuremath{\rho}$ and specific heat ${c}_{p}$ near the superfluid transition of $^{4}\mathrm{He}$ when confined in an array of $(2\text{ }\text{ }\ensuremath{\mu}\mathrm{m}{)}^{3}$ boxes at a separation of $S=2\text{ }\text{ }\ensuremath{\mu}\mathrm{m}$ and coupled through a 32.5 nm film. We find that ${c}_{p}$ is strongly enhanced when compared with data where coupling is not present. An analysis of this excess signal shows that it is proportional to the finite-size correlation length in the boxes $\ensuremath{\xi}(t,L)$, and it is measurable as far as $S/\ensuremath{\xi}\ensuremath{\sim}30\ensuremath{-}50$. We obtain $\ensuremath{\xi}(0,L)$ and the scaling function (within a constant) for $\ensuremath{\xi}(t,L)$ in an ${L}^{3}$ box geometry. Furthermore, we find that ${\ensuremath{\rho}}_{s}/\ensuremath{\rho}$ of the film persists a full decade closer to the bulk transition temperature ${T}_{\ensuremath{\lambda}}$ than a film uninfluenced by proximity effects. This excess in ${\ensuremath{\rho}}_{s}/\ensuremath{\rho}$ is measurable even when $S/\ensuremath{\xi}g100$, which cannot be understood on the basis of mean field theory.

We report sorption isotherms and optical measurements for fullerite C 60 /C 70 crystals and C 60 films exposed to helium. The low temperature isotherms show excess sorption above that expected for surface films. We interpret this as intercalation of helium in the fullerite lattice. Our observations suggest that helium is mobile within the crystal, and opens up the possibility of realizing a new type of three-dimensional quantum fluid. Raman measurements are inconclusive on the issue of intercalation

We report measurements of the convective conductance of {sup 4}He films near the Kosterlitz-Thouless transition. Data for 14 films are analyzed over a range of critical temperatures from 1.28 to 2.16 K, and thicknesses 11.7 to 156 A. We obtain good agreement using two different methods of analysis with the predicted behavior of the dynamic theory. The exponential divergence is observed up to six decades in conductance and one decade in reduced temperature. We find that the parameter {ital b}, which determines the sharpness of the divergence, and also the cusp in the superfluid density increases with film thickness. This is consistent with the growth of the three-dimensional correlation length. We find also that the ratio of diffusion constant to the square of the vortex core radius, {ital D}/{ital a}{sup 2}, is a decreasing function of film thickness. We compare this with measurements in which {ital D} is obtained directly. We also report measurements of the nonlinear dependence of the conductance below the transition. These are shown to be consistent with measurements above the transition.

We have measured the heat capacity of (3)He-(4)He mixtures confined in films of thickness 48.3 and 986.9 nm. The confinement is defined by direct bonding of two silicon wafers. The heat capacity is measured using an ac technique and then transformed to correct for exponent renormalization effects. The data address the expected universal critical behavior along the lambda line as function of (3)He concentration. We discuss the results of several analyses of the data, and we show that a universal collapse can be achieved for all the mixtures. However, this is on a locus which differs from that of the pure system. An alternative analysis is also presented which yields collapse of all the data under certain assumptions. We believe these data are the first to test universality of finite-size scaling for the specific heat along a locus of transitions.

Mesures de transport thermique dans des couches minces 4 He au voisinage de la transition superfluide

Measurements of the thermal conductance of /sup 4/He films near the superfluid transition indicate nonlinear behavior below T/sub c/, as well as above T/sub c/, for sufficiently large velocities. Below T/sub c/ the behavior is characterized by an exponential dependence on film velocity. This suggests that, for our experiment, depinning is the dominant mechanism for free-vortex generation.

We have measured the heat capacity of $^{3}\mathrm{He}$ in films of $^{4}\mathrm{He}$ as thin as 10 A\r{} formed on a Nuclepore filter substrate. At low temperatures, where the $^{3}\mathrm{He}$ is in the lowest state as far as motion perpendicular to the film surface, we find that the $^{3}\mathrm{He}$ undergoes a transition from a dilute phase to a dense phase. We have observed this transition for films of $^{4}\mathrm{He}$ of 12.3- and 10-A\r{} thickness and for coverages of $^{3}\mathrm{He}$ below about 0.2 atomic layers. For thicker $^{4}\mathrm{He}$ films, and higher $^{3}\mathrm{He}$ coverages, the $^{3}\mathrm{He}$ remains homogeneously spread out over the surface of the $^{4}\mathrm{He}$. The striking characteristic of the transition is the sudden onset of linear temperature dependence with a slope which is proportional to the amount of $^{3}\mathrm{He}$ in the calorimeter. This is consistent with the formation of islands of a dense two-dimensional phase which grows in extent proportionately to the amount of $^{3}\mathrm{He}$. Two puzzling aspects of our results are the lack of a significant heat-capacity jump at the transition and, based on a linear extrapolation of the data to zero temperature, a substantial amount of missing entropy.

We present measurements of the surface tension sigma (T) and surface entropy-dsigma/dT of superfluid helium in the temperature range from 0.3 to 2.1 K. The data were obtained by a method in which changes in the capillary rise of the liquid in a parallel plate capacitor are balanced by an electric field which keeps the meniscus stationary. The method is capable of high precision since it does not suffer from many of the errors introduced by imperfections in the capacitor plates. The data show that, even at the lowest temperatures, there are systematic deviations from the Atkins theory of the temperature dependence of sigma, although the theory appears to be correct in the limit that the temperature goes to zero. A new version of the theory, which includes the effects of compressibility and the curvature dependence of the surface tension, is in much better agreement with the data for temperature up to approx. 1 K.

We have measured the specific heat near the $\ensuremath{\lambda}$ transition of pure $^{4}\mathrm{He}$ and of five $^{3}\mathrm{He}$-$^{4}\mathrm{He}$ mixtures up to a mole fraction of 0.39 $^{3}\mathrm{He}$ in $^{4}\mathrm{He}$. Our data for $^{4}\mathrm{He}$ confirm the results of Ahlers revealing an asymmetry in the exponents above and below ${T}_{\ensuremath{\lambda}}$ when the specific heat is represented by a simple-power-law temperature dependence. Our results for these exponents ($\ensuremath{\alpha}=0.012\ifmmode\pm\else\textpm\fi{}0.002$ and ${\ensuremath{\alpha}}^{\ensuremath{'}}=\ensuremath{-}0.012\ifmmode\pm\else\textpm\fi{}0.004$) differ somewhat from Ahlers's. Our results can be reconciled with the requirement of scaling ($\ensuremath{\alpha}={\ensuremath{\alpha}}^{\ensuremath{'}}$) only by supposing substantial contributions to ${C}_{p}$ are made by singular correction terms to a simple power law. The measured specific heat of the mixtures richest in $^{3}\mathrm{He}$ appears to be finite, continuous, and cusped at the $\ensuremath{\lambda}$ line. These qualitative features have been termed "renormalization" by Fisher. An analysis of our mixture data with a power-law temperature dependence does not yield a fully renormalized exponent, but rather an effective exponent. We have calculated the following derivatives at the $\ensuremath{\lambda}$ line: ${(\frac{\ensuremath{\partial}s}{\ensuremath{\partial}T})|}_{p,\ensuremath{\lambda}}$, ${(\frac{\ensuremath{\partial}\ensuremath{\varphi}}{\ensuremath{\partial}T})|}_{p,\ensuremath{\lambda}}$, and ${(\frac{\ensuremath{\partial}x}{\ensuremath{\partial}T})|}_{p,\ensuremath{\lambda}}$. We have used these derivatives to calculate the specific heat along paths of constant pressure and constant relative chemical potential ${C}_{p\ensuremath{\varphi}}$. This specific heat behaves very much like ${C}_{p}$ of pure $^{4}\mathrm{He}$ supporting the idea of universality for the specific-heat exponents. It is also true that the same asymmetry in the branches above and below ${T}_{\ensuremath{\lambda}}$ which is observed in pure $^{4}\mathrm{He}$ is retained in the mixtures. The persistence of the asymmetry of ${C}_{p\ensuremath{\varphi}}$ as one moves along the $\ensuremath{\lambda}$ line towards increasing $^{3}\mathrm{He}$ concentration (at the saturated vapor pressure of the mixtures) is analogous to the persistence of the asymmetry of ${C}_{p}$ as one moves along the $\ensuremath{\lambda}$ line towards increasing pressure in pure $^{4}\mathrm{He}$. In both cases a unique reconciliation of the asymmetry with scaling must await better predictions of the form of the corrections to scaling. We have used our calculated ${C}_{p\ensuremath{\varphi}}$ to construct the derivative ${(\frac{\ensuremath{\partial}x}{\ensuremath{\partial}T})|}_{p,\ensuremath{\varphi}}$ hence paths of constant $\ensuremath{\varphi}$ on the $x\ensuremath{-}T$ plane, as well as the derivative ${(\frac{\ensuremath{\partial}x}{\ensuremath{\partial}\ensuremath{\varphi}})|}_{p,T}$.

New measurements of heat capacity for /sup 3/He adsorbed on /sup 4/He films are presented. It is found that for the thinnest /sup 4/He film used, and starting at a /sup 3/He coverage of 0.058 layer, 3.7 x 10/sup -4/ A/sup -2/, the data show a very sudden onset of degeneracy. These data are consistent with phase separation in the two-dimensional layer of /sup 3/He at the surface of the /sup 4/He film.

We present new measurements of the superfluid density of /sup 4/He confined between sheets of Mylar at 4600 A average separation. These data show a full range of behavior, from bulk, to finite size, to two dimensional. We analyze these data, as well as those from three other experiments, to test predictions of finite-size scaling theory. We use a scaling function from the Ginzburg-Pitaevskii-Mamaladze theory, as well as a function we suggest in analogy to the work of Josephson. We find that only this latter function is consistent with the data. Furthermore, we find that the deviations from bulk behavior do not scale with the bulk-correlation-length exponent. We find this to be in quantitative agreement with earlier results for the specific heat of confined helium.

We have measured the convective conductance of saturated helium films at the superfluid transition. Our data show that the Kosterlitz-Thouless features of the transition established for thinner films are retained for all the films we have measured up to 156 A\r{}. The finite-size scaling hypothesis is examined, and it is found that the shift in transition temperature is governed by an exponent less than that of the three-dimensional correlation length. This result agrees with earlier results of the specific heat of films. A comparison of the conductance and specific-heat data shows that for films of equal thickness the divergence in the conductance is well below the temperature of the specific-heat maximum. While this is expected for the superfluid transition in two dimensions, we point out, however, that the specific-heat maximum for the thick films is not due to two-dimensional effects. We find that at both of these temperatures the three-dimensional phase correlation length would be substantially less than the thickness of the film.

We report measurements of the superfluid density of $^{4}\mathrm{He}$ confined between two Si wafers. These are the first measurements of helium confined in a sufficiently well-defined planar geometry to show a crossover from three-dimensional-like to finite-size to two-dimensional behavior. Data for confinement in 0.106, 0.509, 2.8, and 3.9-\ensuremath{\mu}m-thickness cells are analyzed for scaling with the exponent of the bulk correlation length, \ensuremath{\nu}. We find that this scaling does not work: An exponent different from \ensuremath{\nu} is required. We discuss these results in light of finite-size scaling predictions and earlier measurements.

A connection between surface fractal dimensionality and the critical behavior of confined /sup 4/He at the superfluid transition is suggested. It is shown that in the specific case of Nuclepore filters the disagreement with bulk-correlation-length scaling can be resolved if one ascribes a fractal dimension to the confining surface of about 2.34. Explicit scaling functions for both the specific heat and the superfluid density are suggested. Measurements of adsorption isotherms for 0.2-..mu..m filters support this fractal conjecture and yield a surface dimensionality of 2.24 +- 0.02.

We present an analysis of specific-heat data of $^{3}\mathrm{He}$-$^{4}\mathrm{He}$ mixtures at the $\ensuremath{\lambda}$ transition in which a trial function with a correction term to the leading singularity is used. For mixtures up to 0.39 mole fraction of $^{3}\mathrm{He}$ in $^{4}\mathrm{He}$ we find a universal leading exponent $\ensuremath{\alpha}={\ensuremath{\alpha}}^{\ensuremath{'}}=\ensuremath{-}0.022$ and a universal leading amplitude ratio of $\frac{A}{{A}^{\ensuremath{'}}}=1.088$. These results are in agreement with theoretical expectations and other experimental results along the \ensuremath{\lambda} line as a function of pressure. The data at pure $^{4}\mathrm{He}$ and saturated vapor pressure appear to show a small deviation from universal behavior.

Two superfluid phase transitions in $^{3}\mathrm{He}$-$^{4}\mathrm{He}$ films have been observed. Both transitions, $A$ and $B$, possess Kosterlitz-Thouless characteristics, but phase $B$ has a much less pronounced onset signal. At constant $^{4}\mathrm{He}$ coverage the transition temperature of $A$ decreases while that of $B$ increases upon addition of $^{3}\mathrm{He}$. We discuss possible interpretations of these results based on existing theories and connections with other measurements.

We report measurements of the convective conductance of /sup 3/He-/sup 4/He films near the superfluid transition. This thermal response is tested for the critical behavior observed in pure /sup 4/He films. We find that this is preserved for mixtures. The parameters b and D/a/sup 2/, however, show a strong renormalization, and an unusual /sup 3/He dependence. The conductance at fixed T-T/sub c/ decreases upon addition of /sup 3/He implying a decrease of the 2D correlation length. We observe a decrease in the maximum value of conductance which we attribute to a residual free-vortex density, even for T

We have measured the mass loading on a torsional oscillator of mixture films of $^{3}\mathrm{He}$ and $^{4}\mathrm{He}$ at coverages near one active atomic layer of $^{4}\mathrm{He}$. These measurements yield information about the superfluid transition of $^{4}\mathrm{He}$ and the effective mass and binding energy of $^{3}\mathrm{He}$. Unlike the situation with submonolayer and multilayer films, where the superfluid transition takes place at a single temperature, we observe for these films a transition in two steps. This confirms a report some time ago of a similar observation by Bishop and Reppy. By comparing the mass loading at T=0 of pure $^{4}\mathrm{He}$ films with that of mixtures, we obtain the $^{3}\mathrm{He}$ effective mass which can be compared with results from the specific heat. We find, in particular, that the effective mass has a maximum as a function of $^{4}\mathrm{He}$ thickness with correct asymptotic values for infinite and zero thickness limits. This maximum coincides very nearly with the thickness of $^{4}\mathrm{He}$ at which the transition into the superfluid state takes place in two steps. In the submonolayer region the effective mass agrees with a density dependence one might expect as an extension of the theory of Pandharipande and Itoh for three-dimensional mixtures. We believe such theory should be able to be done for the two-dimensional case.

We report measurements and analysis of the heat capacity of /sup 3/He in films of /sup 4/He. The data span a range of /sup 3/He coverage from 0.03 to 1 atomic layer and /sup 4/He film thickness from 10 to 45 A. We find that for cases where the /sup 3/He remains homogeneously spread out over the surface of the film, it acts like a two-dimensional gas of Fermi quasiparticles. To analyze our data, we use a model whereby the /sup 3/He retains its two-dimensional degree of freedom along the surface, but is quantized in its motion perpendicular to the surface. For thin films, up to about 25 A, a single excited state within the film is necessary to describe the data satisfactorily. For the thickest films, several excited states become necessary. Equivalently, in this case, one may assume a continuous three-dimensional spectrum. The results of our analysis show that the /sup 3/He on these films behaves quite differently from /sup 3/He at the surface of bulk /sup 4/He. The surface effective mass and excitation energy are functions of coverage and /sup 4/He thickness. This suggests that the /sup 3/He is highly interacting with the strength of the interaction beingmore » controlled by the thickness of the /sup 4/He. For the thinnest films we find that the excitation energy has a minimum as a function of coverage, at about 0.2 layer.« less

We have measured the specific heat of helium near the superfluid transition for films up to 56 A thick and for sample confined to a cylindrical geometry of up to 2000 A in diameter. The dependence of the shift in the transition temperature on size and the growth of the specific-heat maximum do not yield exponents as expected from simple scaling arguments. The data up to t equivalent abs. value(1 - T/T/sub lambda/) = 10/sup -2/ scale according to a form suggested by Fisher, but with an exponent 1/theta = 0.54 +- 0.02.

Measurements and analysis of heat capacity for /sup 3/He in /sup 4/He films at temperatures below 350 mK are reported. The data show that /sup 3/He is less bound to the free surface of the /sup 4/He film than to the bulk /sup 4/He surface, and that it has a larger effective mass. Both of these parameters depend on /sup 3/He surface coverage. The /sup 3/He dissolved within the film behaves as a two-dimensional system for sufficiently thin /sup 4/He films.