Session L26 - Superfluidity of 4He.
FOCUS session, Wednesday morning, March 20
206, Indiana Convention Center

[L26.001] Third Sound Attenuation due to Vortices in Thick Helium Films

Third sound attenuation in thick ^4He films has always been observed to be much greater than theoretical models predict. We suggest a source of the high dissipation. Pinned vortices, possibly created when the superfluid transition is traversed, undergo driven oscillations in the third sound wave flow field. The dissipation is then caused by two related effects. The first is due to the mutual friction between the vortex cores and the normal component. The second, larger contribution, is due to the drag experienced by the vortex-induced surface dimple. Variations in vortex density naturally explain the observed lack of reproducibility seen in measured attenuation. A vortex density on the order of 10^17 m^-2 is needed to account for dissipation reported in several experiments.

[L26.002] Propagation of Third Sound through Sets of CaF_2 Scatterers

We are investigating the transmission of multiply scattered third sound. We create third sound on ^4He films that are adsorbed to glass substrates with regions of CaF_2 selectively deposited on them. The third sound travels slower on the CaF_2 regions causing these regions to act as a third sound scatterer. We present preliminary results for the third sound transmission spectra from two such substrates. One substrate has a set of scatterers located on a square lattice (ordered) and the other has a set of scatterers with randomly chosen positions (disordered). The ordered substrate spectra shows a clear band/band-gap structure. In contrast, only low frequencies propagate across the disordered substrate. This is likely due to the frequency dependence of the Anderson localization length. As an additional check, we have recorded transmission spectra across uniform glass and uniformly deposited CaF_2 substrates. The results confirm that the transmission behavior is due to the scatterer patterns and not some other effect.

[L26.003] Singularity in the boundary resistance between superfluid ^4He and a solid surface

We report new measurements in four cells of the thermal boundary resistance R between copper and ^4He below but near the superfluid-transition temperature T_\lambda. For 10^-7 \leq t \equiv 1 - T/T_\lambda \leq 10^-4 fits of R = R_0 t^x_b + B_0 to the data yielded x_b \simeq 0.18, whereas a fit to theoretical values based on the renormalization-group theory yielded x_b = 0.23. Alternatively, a good fit of the theory to the data could be obtained if the amplitude of the prediction was reduced by a factor close to two. The results raise the question whether the boundary conditions used in the theory should be modified.

Supported by NASA through Grant NAG8-1757

[L26.004] Pressure Dependence of the Thermal Resistivity of Liquid ^4He in a Confined Geometry near T_\lambda

We present results of measurements of the thermal resistivity R(t,P) of liquid ^4He in a confined geometry near the superfluid transition as a function of the pressure P and reduced temperature t\equiv T/T_\lambda(P) - 1. The confining medium was a micro-channel plate with holes of a uniform radius L=1.0 \mum, and six pressures ranging from saturated vapor pressure (SVP) to 28~bar were used. Our data are consistent with a universal scaling relation between R and t close to T_\lambda(P) which is valid for all pressures. In particular, plotting F=\left(L/\xi_0\right)^x/\nu\left( R/R_0\right) versus X= \left(L/\xi_0\right)^1/\nut, where R_0 and x are the pressure-dependent amplitude and effective exponent of the bulk resistivity, \xi_0 is the pressure-dependent bare correlation length, and \nu=0.6705 is the pressure-independent exponent of the correlation length, causes the data to collapse onto a single curve, a result which is consistent with dynamic finite-size scaling. Other features of the data below T_\lambda(P) will be discussed.

[L26.005] Effects of the van der Waals interaction on the superfluid density of confined ^4Helium

We investigate the effect of van der Waals interactions on the superfluid density of confined helium near T_\lambda for 1D and 0D dimensionality crossover, and compare the results to the 2D case. We estimate the magnitude of this effect using \psi-theory as formulated by Ginzburg and Sobyanin, in which the effect of the wall can be folded into the equation for the order parameter via a spatially-dependent transition temperature. We find that for radii equal to the film thickness in the 2D case, the effects for spherical and cylindrical confinements are smaller for small values of the scaling variable than for planar confinements. This work is supported by the National Science Foundation, DMR9972287.

[L26.006] 0D crossover in the specific heat of confined helium.

We report measurements of the specific heat of ^4He confined in 1\mum^3 boxes patterned in SiO_2. This system crosses from 3D behavior to 0D behavior as the critical temperature is approached. This has a remarkable effect on the heat capacity maximum as seen by a pronounced rounding and a shift to a temperature much lower then the transition of the bulk system. We plot the data according to correlation-length scaling theory and compare this to a planar system with the same smallest spatial length. Also the 0D cell, with approximately 10^9 boxes, has a much larger ratio of surface to volume compared to our previous studies of planar systems. This allows us to examine the region where the surface specific heat dominates and compare this to existing theories. We find the data do not reach the expected value in this region and there is a different locus in the region where the scaling variable tL^1/\nu, is greater than 2x10^2. This may be associated with edge contributions to the total free energy. Work supported by the NSF, DMR-9972287.

[L26.007] Bose-Einstein Condensation in Liquid ^4He in Disorder

We present the first neutron scattering measurements of Bose-Einstein condensation in liquid ^4He confined in Vycor. These show that there is definitely a condensate in Vycor with condensate fraction comparable to that in bulk superfluid ^4He, approximately 7.5% at low temperature and SVP^1. The temperature dependence of n_0(T) is also similar to that in the bulk with critical temperature, T_c for BEC, in the range 1.8\,<\,T_c\,<\,2.25\,K. The data are not accurate enough to show whether T_c for BEC in Vycor is the same or greater than T_c\,=\,1.95\,K for superfluidity in Vycor^2. These measurements and corresponding measurements of the elementary excitations^3 of superfluid ^4He in Vycor^1 will be discussed.

\beginitemize \item[1.] H. R. Glyde, R. T. Azuah, and W. G. Stirling, Phys. Rev. B 62, 14 337 (2000) \item[2.] M. H. W. Chan, K.I. Blum, S.Q. Murphy, G.K.S. Wong, and J. D. Reppy, Phys. Rev. Lett. 61, 1950 (1988) \item[3.] H. R. Glyde, O. Plantevin, B. Fåk, G. Coddens, P. S. Danielson, and H. Schober, Phys. Rev. Lett. 84, 2646 (2000) \enditemize

[L26.008] Excitations of Superfluid ^4He at Wavevectors Beyond the Roton

\small We present a Quantum Field Theoretical Model that reproduces the basic features of the temperature dependence of the dynamic structure factor S(Q,ømega) of ^4He as observed in the inelastic-neutron scattering data taken at ISIS(\footnotesize J. V. Pierce, R. T. Azuah, B. F\stackrel\circ)\hboxak, A. R. Sakhel, H. R. Glyde, W. G. Stirling, J. Phys: Cond. Matter, 13(2001) 4421., UK. A range of the wavevectors Q beyond the roton (Q\,>\,2.0 Åis considered. The model is able to reproduce the decrease in the intensity of the single-particle excitation peak with increase of T in the range 0.6\,\leq\,T\,\leq\,2.1\,K. Also, it reproduces the second peak at higher energy representing the single excitation intensity lying in the two excitation band. The model is based on the formulation of S(Q,ømega) of Gavoret and Nozi\graveeres(\footnotesize J. Gavoret and P. Nozi\gravee)res, Ann. Phys., 28, 349-399 (1964). In this formulation, the dynamic susceptibility is separated into a singular part involving the condensate and a regular part involving states above the condensate \chi\,=\,\chi_S\,+\,\chi_R. Here \chi_S\,=\,n\,n_0(T)\,\Lambda G \Lambda, \Lambda is a vertex, G the renormalized single particle Green's function, n the density of ^4He at SVP and n_0(T) the condensate fraction as a function of T. \chi_R(Q,ømega) involves both a single particle-hole and a multiparticle component. All vertices and interactions are assumed T-independent, and only n_0 changes with T. Also, the roton width is accounted for by a momentum (k) and temperature dependent width of the Landau-Khalatnikov form (H. R. Glyde, Excitations in Liquid and Solid helium), Oxford, Clarendron Press, (1994)..

[L26.009] Excitations in liquid ^4He in Geltech silica

\small\baselineskip 0.2cm We have measured the elementary excitations of liquid ^4He confined in Geltech silica for temperatures between 35 mK and 2.5 K using inelastic neutron scattering techniques. Geltech is a 40-50% porous media having 25 Ådiameter pores with at most few percent of the volume made up of larger pores of diameter less than 70 ÅWe observe well defined phonon-roton (p-r) excitations at all wave vectors Q investigated (0.4\leq Q \le 2.1 ÅAlso observed are 2D layer modes propagating in the liquid layers adjacent to the media walls. These 2D modes are identified as layer modes by measuring the dynamical structure factor of liquid ^4He as a function of filling of the Geltech. At full filling the energies and lifetimes of the 3D p-r modes are the same as those in superfluid ^4He within the current precision. Most interestingly, we observe a well defined p-r excitation above the superfluid-normal transition T_c =0.725 K as determined in a torsional oscillator measurement(\scriptsize S. Miyamoto and Y. Takano, Czech. J. Phys. 46), 137 (1996). Observation of a well defined maxon-roton above T_c in Geltech suggests, as in the case of Vycor(\scriptsize H. R. Glyde, O. Plantevin, B. Fåk, G. Coddens, P. S. Danielson, and H. Schober, Phys. Rev. Lett. 84), 2646 (2000), that there can be localized Bose-Einstein condensation in porous media with phase coherence on short-length scales above the macroscopic superfluid transition temperature.

[L26.010] Finite-Size Scaling of Thermal Conductivity of Confined Helium

We have studied the thermal conductivity of confined superfluids. using the planar magnet lattice model on lattices H\times H\times L and L\times L \times H with L \gg H. We have applied periodic boundary conditions along the long directions and open along the short directions. We have adopted a hybrid Monte Carlo algorithm to efficiently deal with the critical slowing down and in order to solve the dynamical equations of motion we use a discretization technique which introduces errors only O((\delta t)^6). Our results for the bar-like geometry are consistent with finite-size scaling theory and the thermal resistivity scaling function is in good agreement with the available experimental results for pores.

[L26.011] Submonolayer Molecular Hydrogen on Graphite: A Path Integral Monte Carlo Study

We have used path integral Monte Carlo (PIMC) to simulate molecular hydrogen on graphite at submonolayer coverage. First we use a flat substrate and we study the first layer for various values of the coverage up to layer completion. Second we introduce the full H_2-graphite interaction, i.e., we include the effects of substrate corrugation. We calculate the energy as a function of coverage, contour plots of the molecule probability distribution, the pair distribution function, the static structure function and the specific heat. Using these observables we have verified the phases of the experimentally determined rich phase diagram of the submonolayer up to layer completion.

Part L of program listing