Superfluidity of solid4He

Using a procedure suggested by Leggett, an upper bound to the superfluid fraction in ground state solid ⁴ He slightly above the melting density is obtained numerically. The value obtained is 0.3±0.1. To judge the usefulness of this upper bound, we examine the conditions under which a symmetrized product of single-particle functions times a Jastrow function exhibits ODLRO, a necessary and sufficient condition for superfluid flow. It is found that ifU _ij (U _ij=? φ _i (x)φ _j (x) dx, and φ _i (x) is a single-particle wave function centered on the pointi) satisfies σ′_i U _ij>x, wherex varies from unity for long rangeU _ij (i.e.,U _ij decreases slowly enough asR _i?R_j increases) to a value of 12/7 for nearest-neighbor overlap only in the hcp lattice, then there is ODLRO, but not otherwise. Therefore, if the accepted single-particle functions are the true ones, then there is no ODLRO in solid ⁴ He, since the overlap is too small. We have explored the possibility of adding a flat tail, of magnitude λ′(VN)^?1/2 to the accepted single-particle functions. It is shown that if λ → 1 [λ ² =(λ′) ² +2(vNV ^?1)^1/2, andv=(? φ_i(x)dx)²], the system wave function becomes a pure Jastrow function, whereas if λ²?1??2×10 ^?1 , we have in effect the case where λ′=0; furthermore, there is ODLRO if λ ² ?1～?2×10 ^?1 . It is also concluded that the superfluid fraction upper bound of 0.3±0.1 obtained here as well as one suggested by Leggett are not very useful. We have not attempted to establish if there is some value of λ satisfying the above inequality such that the ground-state energy is lower than the value it takes for λ′=0.     

Solid Nitrogen Confined in Porous Glass

N ₂ condensed into nanoporous glass has been investigated by X-ray diffraction and adsorption/filling isotherms. The material in the pores consists of an amorphous layer at the pore walls and quasi–bulk material in the center of the pores. The freezing temperature of the bulk component is reduced. Its structure is hcp down to lowest temperatures with a stacking fault probability as large as 0.3. Thus the transition hcp–Pa3 of the bulk solid is suppressed.     

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     

Towards Superfluidity of 3He Diluted by 4He

Search for the superfluid state of dilute ³He dissolved to ⁴He is one of the major remaining problems of low temperature physics. We describe our two experiments designed to pursue the lowest achieved temperature in such mixtures essentially below the values reported before.     

Sound Experiments on Superfluidity of 3He in Highly Porous Aerogels

We have carried out sound experiments on superfluid ³ He in three highly porous aerogels with different porosities. Two of the acoustic cells contain aerogels inside the pores in roughly sintered silver powder to avoid the vibration of the aerogel. In these acoustic cells we have detected fourth sound, and extracted the superfluid density from the fourth sound velocity. The effect of the sintered silver on superfluid ³ He was examined by using another acoustic cell which contains the sintered silver without aerogel. The size of the pores in the sintered silver was large enough not to show the size effect of superfluid ³ He and small enough to observe fourth sound of ³ He. In another cell without sintered silver, we have observed second-sound-like signal. The superfluid transition temperatures of ³ He are suppressed more in higher density aerogel. The aerogel density dependence of the suppression of the superfluid transition temperature of ³ He in aerogel can be explained qualitatively by the simple s-wave scattering approximation. However, the superfluid density shows quite different pressure-dependence in different porous aerogels. The reason of this phenomenon is not understood yet.     

Observation of Non-Classical Rotational Inertia in Solid 4He Confined in Porous Gold

No Heading Recent torsional oscillator measurements on solid ⁴He confined in Vycor glass at 62 bars show supersolid response, an abrupt drop in rotational moment of inertia, at 175 mK¹. We have investigated the pore-size dependence of the supersolid behavior by confining solid ⁴He in a different porous host, porous gold, of a considerably larger pore diameter. When solid ⁴He in porous gold is cooled below 0.2 K a sharp drop in the resonant period is found. The supersolid response exhibits a strong dependence on the amplitude of oscillation.PACS numbers: 67.80–s. 67.80 Mg., 0.5.70.Fh, 05.30.Jp     

Phase Separation of Liquid 3He–4He Mixtures in Porous Vycor Glass

We report our recent investigations of the phase separation of liquid ³ He– ⁴ He mixtures in the restricted geometry of porous Vycor glass using pressure measurements. The experimental cell is entirely filled with a Vycor cylinder and closed by a cold valve. We are measuring the pressure versus temperature by means of a capacitive pressure gauge. The results are discussed in comparison with the phase separation of helium mixtures in aerogel, ¹ in particular with respect to the different ratio of substrate surface to liquid volume of both glasses.     

Local Superfluidity in 4He and para-H2 Clusters

No Heading We present a new definition of local superfluidity around impurities in quantum fluids that provides a consistent analysis of the response of the inhomogeneous fluid density to the impurity rotations. This definition is based on the local decomposition of the moments of inertia of the fluid, which can be estimated from the projected area of exchange-coupled Feynman paths in path integral Monte Carlo calculations. Application to helium droplets doped with a planar phthalocyanine molecule shows that the first solvation layers parallel to the molecular plane consist of localized helium atoms that are totally inert to superfluid response, while the second solvation layers and capping regions at the end of the molecule exhibit partial and anisotropic superfluidity. Application to weakly bound complexes of the linear OCS molecule with para-hydrogen molecules shows evidence for the existence of molecular supersolids. We find that five H₂ molecules constitute a single ring around OCS which possesses both a solid-like pair correlation function and a complete superfluid response to rotation around the molecular axis below T ~ 1 K.PACS numbers: 36.40.–c, 36.40.Mr, 67.40.–w. 67.40. Yv     

Superfluidity of Pure 3He and Mixtures of 3He and 4He in Aerogel

We describe new torsional oscillator experiments on ³ He confined in 98.2% open aerogel. In one, we monitored the superfluid fraction of pure ³ He at T << T _c while we gradually changed the sample pressure. The resulting change in density alters ₀ of the superfluid ³ He relative to the distribution of the length scales (correlations) of silica in the aerogel. We observed a T = 0 normal-to-super fluid transition at a pressure of about 6.5 bar, in marked contrast to the bulk where liquid ³ He is superfluid at all pressures. In the second experiment, we measured the temperature dependence of the ³ He _s at a pressure of 21.6 bar with different amounts of ⁴ He present in the cell. Adding 2-3% ⁴ He slightly increases both T _c and _s . We found that for ⁴ He concentrations between 2% and 34%, the ³ He T _c increases by a very small amount. However, _s , which for pure ³ He in aerogel at 0.5T _c is no more than 11%, falls by another factor of 7. This behavior (constant T _c , reduced _s ) is similar to that observed in granular superconducting films where the long-range order is controlled by phase coherence between adjacent grains.     

Large Boundary Magnetism and Superfluidity of Liquid 3He in Nanometer-sized Porous Alumina

Continuous-wave NMR measurements were performed for liquid ³He in porous alumina with nominal pore size of 20 nm in diameter, at temperatures down to 0.3 mK. The signal is composed of two contributions: from the liquid and from the boundary solid layer of ³He on the alumina’s surface. The latter shows a well-known ferromagnetic tendency and signal intensities can be fitted to a Curie-Weiss law in the high temperature region. The obtained Weiss temperatures are 0.18 and 0.50 mK at 7.5 and 28 bar, respectively. ⁴He coverage (4 monolayers) completely eliminates boundary signal between 7.5 bar and 32.5 bar. The residual liquid signal shows frequency shift and broadening below superfluid transition temperatures depending on liquid pressures. The obtained P-T phase diagram well resembles that of bulk liquid ³He in spite of the very narrow pore-size comparable to the coherence length of superfluid ³He.      

Interplay of Non-linear Elasticity and Dislocation-Induced Superfluidity in Solid 4He

The mechanism of the roughening induced partial depinning of gliding dislocations from ³He impurities is proposed as an alternative to the standard “boiling off”. We give a strong argument that ³He remains bound to dislocations even at large temperatures due to very long equilibration times. A scenario leading to the similarity between elastic and superfluid responses of solid ⁴He is also discussed. Its main ingredient is a strong suppression of the superfluidity along dislocation cores by dislocation kinks (D. Aleinikava, et. al., arXiv:0812.0983, 2008). These kinks, on one hand, determine the temperature and ³He dependencies of the generalized shear modulus and, on the other, control the superfluid response. Several proposals for theoretical and experimental studies of solid ⁴He are suggested.     

Slippage of 4He Films and Precursor Phenomenon of Superfluidity

We have carried out quartz crystal microbalance (QCM) experiments for ⁴He films on an exfoliated single-crystalline graphite using a 32 kHz tuning fork, and have measured the temperature dependence of the resonance frequency and the Q value for various areal densities and oscillation amplitudes. Comparing with the previous experiments for Grafoil, the decoupling of the films due to the slippage or the superfluidity was larger than that of Grafoil, and the competition between the slippage and the superfluidity was observed in three-atom thick films. Furthermore, it was found that the slippage is suppressed gradually at higher temperature than the superfluid onset T _c , and that the relaxation time decreases at low temperatures while it obeys the Arrhenius law at high temperatures. These results suggest a precursor to the superfluidity of ⁴He films.     

4He in Nano-porous Media: Superfluidity and Quantum Phase Transition

This paper reviews recent findings of novel phenomena in ⁴He confined to a nano-porous glass. We examined pressure–temperature (P-T) phase diagram of ⁴He confined in a porous Gelsil glass that had nanopores 2.5 nm in diameter, by torsional oscillator and pressure studies. The obtained phase diagram is fairly unprecedented the superfluid transition temperature approaches zero at 3.4 MPa, and a novel nonsuperfluid phase exists between the superfluid and solid phase. These observations indicate that the confined ⁴He undergoes a superfluid-nonsuperfluid-solid quantum phase transition at zero temperature. We propose that the nonsuperfluid phase may be a localized Bose-condensed state in which global phase coherence is destroyed by a strong correlation between the ⁴He atoms or by a random potential. ⁴He in nanospace is an excellent model system for studying a strongly correlated Bose liquid and solid in a confinement potential.     

A New Approach to Bose Condensation and Superfluidity in 4He

An investigation is made of the implications that the presence of a Bose condensate (BC) has for the form of the many particle Schröedinger wavefunction. It is shown that many particle wavefunctions of states which contribute to the BC, contain long range structure in the position space of each particle. It follows from the requirement that the wavefunction is single valued that, in the presence of a BC, the angular momentum of each particle must be quantised over macroscopic length scales. The paper thus provides a new and simple proof from first principles, that Bose condensation implies macroscopic quantum behaviour. It is shown that this behaviour can be described in terms of the occupation by each particle of the same single particle-like macroscopic wavefunction. The structure in position space of this wavefunction is investigated, using a well known model of the many particle wavefunction for the ground state of⁴He. The model predicts that the probability density of each particle is delocalised in the presence of a BC, occupying all spaces in the sample volume, from which the particle is not excluded by the hard core interaction with other particles.     

Superfluidity of 4He Adsorbed on Nanoporous Activated Carbon Fibers

⁴He confined in nanoporous media is one of the most interesting nano-sized systems in the context of an interacting Bose system. In the present work, we study superfluidity of ⁴He adsorbed in nanoporous activated carbon fibers (ACFs). Up to a ⁴He coverage of n=22.6 μmol m⁻², no superfluidity is observed. Over 23.7 μmol m⁻², superfluid transition is observed at T _c ∼550 mK. With an increase in n the superfluid density enhances, but T _c is independent of n. These observations indicate that the thickness of the superfluid ⁴He films on the pore wall is restricted by a slit type pore shape of ACFs.     

Superfluidity of4He films adsorbed on hydrogen plated graphite

The superfluidity of⁴He on graphite with various preplatings of HD is under investigation using a torsional oscillator. Results for a bilayer of HD follow a similar pattern to those obtained earlier on pure⁴He films and are consistent with third sound measurements on graphite plated with a bilayer of hydrogen. In our case the first⁴He layer solidifies, consistent with behaviour observed in NMR studies of³He on a similarly prepared substrate. At a coverage of 11nm^–2 there is the onset of a region in which the transition temperature increases rapidly with coverage and the transition itself becomes sharper. At certain coverages pronounced signatures have been observed in the period shift and dissipation, which may indicate a further phase transition in the film at lower temperatures.     

Compressibility of 4He Liquid Confined in Nuclepore

Adding and removing ⁴ He from an experimental cell which contains the porous material Nuclepore results in capillary condensation, hysteresis and avalanches. The volume of liquid in the nearly cylindrical pores is monitored with a capacitance technique. For the situation when all of the pores are full, the initial removal of ⁴ He from the cell results in a slight non-hysteretic decrease in the capacitance, which we attribute to the isothermal compressibility of ⁴ He. As ⁴ He atoms are removed, the surface tension at the meniscus applies a negative pressure to the liquid in the filled pores, which results in a reduction of the density and a decrease in the capacitance. We present results for ⁴ He capillary condensed in 2000 Å pore diameter Nuclepore.     

Dissipation and Phase Slip in Confined Superfluid 4He

We give a brief summary of some results that are to appear elswhere. We have studied a vortex-related mechanism for the non-vanishing thermal resistance well below the bulk lambda point of liquid ⁴He confined in a long cylinder. Here we outline the main concept of the proposed physical mechanism. It involves the non-equilibrium distribution of vortices in the steady state when a small heat current flows along the cylinder axis. We have found that the probability of the saddle-point vortex configuration, which depends exponentially on the length of the vortex, scaled in units of the superfluid correlation length, is the dominant factor in the thermal resistance.     

Dielectric Properties of Porous Reaction-boned Si3N4 Ceramics with Controlled Porosity and Pore Size

This paper presents the microwave dielectric properties of reaction bonded porous silicon nitride ceramics with variant porosity and pore size, which were prepared by adding pore-forming agent grains into the silicon powders. The experimental results show that the dielectric constant and the dielectric loss of the samples reduce evidently with increasing porosity in the sample. When the porosity is constant, the dielectric constant and the dielectric loss of the ceramics decrease visibly as the pore size increases. Among all the obtained samples, the minimum dielectric constant is about 2.4.     

The Superfluid Transition and Vortex Dynamics in Submonolayer Superfluid 4He Films in Porous Glass Under Rotation

A combination of a rotating dilution refrigerator and high-Q torsional oscillator technique has been used to study dynamics of vortices in thin ⁴ He films adsorbed on the porous glass (d=1m pore size). Under rotation an additional dissipation peak with the amplitude proportional to the angular velocity is seen at the middle of the superfluid transition, on the low temperature side of the stationary peak which is present even at =0. We attribute this peak to the 3D Type vortices created in multiply connected ⁴ He film by the rotation. Peak shape of the rotation-induced dissipation could be interpreted as a freezing of the 3D vortices well below T _c