On the Stability of Small Vacancy Clusters in Solid 4He

We study numerically properties of multiple vacancies in solid ⁴He at zero temperature. Up to four vacancies were introduced into the solid through incommensuration between the number of available lattice sites and the actual number of atoms. Vacancy-vacancy correlation function increases at very short distances indicating effective vacancy attraction between vacancies located on nearby lattice sites. The decay of the pair correlation function at large distances puts an upper bound on the absolute value of the binding energy varying from 4 mK at melting density to 150 mK at the highest considered density $\rho=32.2~\mbox{nm$^{-3}$}$ , and no lower bound; either the four-vacancy clusters are unbound, or are bound too weakly for the temperatures of the supersolid experiments.     

The Formation and Melting of 3He Clusters in Phase-Separated Solid 3He-4He Mixtures

Melting pressure measurements have been made on the ³ He-rich phase formed by cooling a solid mixture of 0.6% ³ He in ⁴ He through phase separation, at pressures between 2.78 and 3.56 MPa. For comparison, simultaneous observations were made with the mixture confined in the pores of a silver sinter and in an open volume connected to the same fill-line. Samples in the sinter cell solidify at higher pressures than the open cell and equilibrate more quickly. Both cells exhibit hysteresis between melting and freezing temperatures, and the transitions are broader in the open-volume cell. Relative to pure ³ He, the melting pressure is elevated by as much as 60 kPa in the sinter cell and 20 kPa in the open cell. The size of the pressure change on melting indicates that a large fraction of the ³ He remains solid at pressures below the melting curve, and this effect is more pronounced in the sinter cell. Measurements are in progress to measure the magnetisation through the magnetic ordering transition.     

Specific Heat Anomaly in Solid 3He due to Vacancy Waves

We observed the excess specific heat (anomaly) other than nuclear origins above 10 mK in bcc solid ³ He of 24.21 cm ³/mole. We checked whether it arises from spin polarons due to vacancies out of equilibrium by applying a strong magnetic field, in which vacancies should diffuse and vanish due to high polarization. The specific heat is the same before and after applying a magnetic field of 10 T. This fact indicates that vacancies did not vanish even in a strong field or the anomaly arises from the origin different from vacancies.     

Scattering of 3He and 4He Atoms from 4He Clusters

We develop a microscopic theory of elastic and inelastic scattering and sticking of ³ He and ⁴ He atoms impinging on superfluid ⁴ He clusters. A number of essential aspects must be observed in a physically meaningful and reliable theory of such scattering processes. These are all connected with multiparticle processes, particularly the possibility of energy loss. These processes are (a) the coupling to low-lying excitations which is manifested in a finite imaginary part of the self energy, (b) the interaction with roton–like excitations and the broadening of the roton minimum due to finite–size effects, and (c) the discreteness of low–lying excitations in helium clusters.     

Vortices in Doped 4He Clusters

We investigate the properties of liquid ⁴ He_N clusters hosting a quantized vortex pinned to a dopant atom (Ne or Xe) or molecule (SF ₆ or HCN). A density functional theory is used to calculate the stationary configurations of pure and doped clusters, with and without vortex, up to N=1000. A liquid drop formula is then proposed that accurately describes the total energy of the complex and allows one to extrapolate the results to larger N values. We find that forming a dopant+vortex+ ⁴ He_N complex is energetically favored below a critical size N _cr , which strongly depends on the type of dopant.     

Adsorption of 4He N and 4He N 3He Clusters on Cesium

The ground-state properties of helium clusters ⁴He _N and ⁴He _N ³He, for N≤ 40, adsorbed on the surface of cesium are studied using variational and diffusion Monte Carlo calculations. Binding properties are determined using two different Cs–He interaction potentials. For the smallest clusters, self-binding on a Cs surface is stronger than in two or three dimensions. For N > 10 self-binding in three dimensions is stronger than on Cs for both types of Cs–He interaction potential considered. The obtained binding energies and structure are compared to results of recent density functional calculations. The emergence of edge states of ³He atom, localized along the contact line of ⁴He cluster with a cesium surface, is studied. First indication that ³He atom prefers to be close to the contact line appears already for the ⁴He₃ ³He cluster.     

Charge Transport in Solid 4He

With the help of a new experimental technique strong anisotropy of the mobility of ions has been observed in hcp ⁴ He crystals. The mobility of positive ions in the direction of the six-fold axis is found to be 200 times higher than in the perpendicular direction. Activation energies of the mobility have been measured in both principal directions. They are equal to: 5.3K in the direction of the C₆-axis and 11K in the perpendicular direction. The behaviour of the ions' velocity in the strong electric field regime is also studied as a function of the orientation.     

Isochoric Compressibility of Solid 4He

We have performed experiments in which we inject atoms into hcp, solid ⁴He contained in a cell of fixed volume at pressures greater than the bulk melting pressure. We measure the change in pressure of the solid in response to the injection, which gives a measure of the isochoric compressibility. We show that at T??700?mK the solid undergoes very little growth and is incompressible. With decreasing temperature the compressibility rises, saturates near T??400 mK and may show weak evidence of a decrease near T??250 mK. Measurements at lower temperatures are necessary to fully test the predictions.     

Elastic Properties of Solid 4He

The shear modulus of solid ⁴He increases below 200 mK, with the same dependence on temperature, amplitude and ³He concentration as the frequency changes recently seen in torsional oscillator (TO) experiments. These have been interpreted as mass decoupling in a supersolid but the shear modulus behavior has a natural explanation in terms of dislocations. This paper summarizes early ultrasonic and elastic experiments which established the basic properties of dislocations in solid helium. It then describes the results of our experiments on the low temperature shear modulus of solid helium. The modulus changes can be explained in terms of dislocations which are mobile above 200 mK but are pinned by ³He impurities at low temperature. The changes we observe when we anneal or stress our crystals confirm that defects are involved. They also make it clear that the shear modulus measured at the lowest temperatures is the intrinsic value—it is the high temperature modulus which is reduced by defects. By measuring the shear modulus at different frequencies, we show that the amplitude dependence depends on stress in the crystal, rather than reflecting a superfluid-like critical velocity. The shear modulus changes shift to lower temperatures as the frequency decreases, showing that they arise from a crossover in a thermally activated relaxation process rather than from a true phase transition. The activation energy for this process is about 0.7 K but a wide distribution of energies is needed to fit the broad crossover. Although the shear modulus behavior can be explained in terms of dislocations, it is clearly related to the TO behavior. However, we made measurements on hcp ³He which show essentially the same modulus stiffening but there is no corresponding TO anomaly. This implies that the TO frequency changes are not simply due to mechanical stiffening of the oscillator—they only occur in the Bose solid. We conclude by pointing out some of the open questions involving the elastic and TO behavior of solid helium.     

A New Anomaly in Solid 4He

A new anomaly in the acoustic properties of solid⁴He has been observed when as little as a few parts per million of³He impurities are added. We show that the specific properties of the anomaly, can be explained by a continuous (second order) phase transition from a Bose condensed state above a critical temperature to a normal state below it. In this model the Bose particles which condense are long lived, thermally activated excitations.     

Vortex Dynamics in hcp Solid 4He

The peculiar features noted in (Penzev et al. in Phys. Rev. Lett. 101: 065301, 2008) we conjecture are evidence of a vortex fluid state in solid He. We suggest to analyze this state by means of the dynamics of quantized vortices, as used for the tangle of vortices in superfluid turbulence. We introduce parameters of the vortex tangle dynamics, e.g., relaxation time for the drift of lines in parallel to the torsional oscillation axis. We briefly discuss the transition from the supposed vortex fluid state into the supposed supersolid state (Shimizu et al. in Phys. Rev. Lett., arXiv:0903.1326).     

Shear Modulus in Viscoelastic Solid 4He

The complex shear modulus of solid ⁴He exhibits an anomaly in the same temperature region where torsion oscillators show a change in period. We propose that the observed stiffening of the shear modulus with decreasing temperature can be well described by the response of glassy components inside of solid ⁴He. Since glass is an anelastic material, we utilize the viscoelastic approach to describe its dynamics. The viscoelastic component possesses an increasing relaxation as temperature decreases. The response functions thus derived are identical to those obtained for a glassy, time-delayed restoring back-action. By generalizing the viscoelastic equations for stress and strain to a multiphase system of constituents, composed of patches with different damping and relaxation properties, we predict that the maximum change of the magnitude of the shear modulus and the maximum height of the dissipation peak are independent of an applied external frequency. The same response expressions allow us to calculate the temperature dependence of the shear modulus?? amplitude and dissipation. Finally, we demonstrate that a Vogel-Fulcher-Tammann (VFT) relaxation time is in agreement with available experimental data.     

Kinetics of Liquid 3He Droplets in Solid 4He Matrix

Precise measurements of pressure in the crystal at constant volume were used to obtain the data on growth and dissolution kinetics of liquid ³ He droplets formed as a result of isotopic phase separation of solid ³ He- ⁴ He Mixtures. We studied several crystals with an initial ³ He concentration of 2.05% in the pressure range of 26–27 bar. It is shown that the growth of the liquid droplets during the stepwise cooling of the two-phase crystal is correctly described by the superposition of two exponential processes: diffusion decomposition with a small time constant and strain relaxation with a big time constant. The strain layer near the droplet boundaries is due to a great difference in molar volume between the droplets and the matrix, and leads to a plastic deformation of the matrix and to a non-equilibrium ³ He concentration in the matrix. Under such conditions quantum diffusion is significantly suppressed and ³ He atom transport occurs only as the strain is relaxed.     

The Annealing Process in Solid 4He

We have used a torsional oscillator with square cross section and a resonance frequency of 185 Hz to confirm the nonclassical rotational inertia (NCRI) discovered by Kim and Chan (Nature 427:225, 2004; Science 305:1941, 2004). We have also found a strong correlation between the NCRI signal and a high dissipation Q ^?1 of 4×10^?6 of the oscillation above the transition temperature. Here, we present preliminary results of the annealing process in ⁴He at a pressure of 26 bar. When holding the temperature constant above 1 K we have observed a immediate rise in the period and a slow decay of the dissipation. The equilibrium value of Q ^?1 decreases with increasing temperature.     

Theoretical Search for Shell Effects in 4He Clusters

An exhaustive analysis of ⁴He clusters at T=0 using the diffusion Monte Carlo method has been carried out searching for possible shell structures. Contrary to previous microscopic calculations, we have focused our attention on a one-by-one number of atoms calculation around the experimental magic numbers N _m. The energy per particle and density profiles are therefore obtained with high resolution. The resugts obtained for the chemical potential as a function of the number of atoms do not show any signature of shell effects around the selected N _m values. Influence on the density profiles is not observed either.     

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     

Study of Solid 4He in Two Dimensions

Defects are believed to play a fundamental role in the supersolid state of ⁴He. We report on studies by exact Quantum Monte Carlo (QMC) simulations at zero temperature of the properties of solid ⁴He in presence of many vacancies, up to 30 in two dimensions (2D). In all studied cases the crystalline order is stable at least as long as the concentration of vacancies is below?2.5?%. In the 2D system for a small number, n _v , of vacancies such defects can be identified in the crystalline lattice and are strongly correlated with an attractive interaction. On the contrary when n _v ?10 vacancies in the relaxed system disappear and in their place one finds dislocations and a revival of the Bose-Einstein condensation. Thus, should zero-point motion defects be present in solid ⁴He, such defects would be dislocations and not vacancies, at least in 2D. In order to avoid using periodic boundary conditions we have studied the exact ground state of solid ⁴He confined in a circular region by an external potential. We find that defects tend to be localized in an interfacial region of width of about 15 ?. Our computation allows to put as upper bound limit to zero-point defects the concentration 3×10^?3 in the 2D system close to melting density.     

Vortex-Loops and Solid Nucleation in Superfluid 4He and 3He

We propose a new model for the nature of the nucleation of solid from the superfluid phases of ⁴He and ³He. Unique to the superfluid phases the solid nucleation involves an extremely fast solidification front. We depart from the usual quasi-static treatment of solid nucleation by proposing that the nucleation of a solid seed is helped by the simultaneous nucleation of vortex-loops in the superfluid around it. It is the composite entity which is nucleated out of the over-pressurized liquid. This occurs when the local release of pressure creates a velocity field in the superfluid which in turn facilitates the nucleation of vortex-loops. The kinetic energy gain of this process balances the surface tension, as the solid surface is quickly covered by many vortex-loops (hairy snow-ball). We show that this scenario gives good agreement with many experiments on heterogeneous nucleation, where the energy barrier is found to differ with the classical theory of homogeneous nucleation by 8 orders of magnitude. We propose several experiments that could show the involvement of vortices with solid nucleation.     

Phase Separation Line for Solid Mixtures of 3He in 4He

The excess pressure due to the phase separation of solid mixtures of ³He in ⁴He held at a constant volume was measured and used for constructing the phase separation diagram of this system. We obtained high-quality homogeneous samples of the solid mixtures after several cycles of cooling down and heating up the two-phase crystal. This gave reliable and reproducible experimental data without hysteresis efects. We compared the phase diagram line obtained with various theoretical approaches, which describe the phase separation of the helium isotope mixtures. The regular solution model can not describe the experimental data well and neither can the asymmetrical Mullin's model. Good agreement is observed only with the theory of Edwards and Balibar which takes into account the difference between the crystal symmetry (hcp and bcc) of the coexisting phases.     

Dielectric Constant Measurements of Solid 4He

Careful measurements of the dielectric properties of solid ⁴He have been carried out down to 35 mK, considerably lower than the temperature range of previous studies. The sample was prepared from high purity gas with ³He concentrations of the order of 200 ppb and were formed by the blocked capillary method. The molar volume of the sample was 20.30 cm³. The dielectric constant of the samples was found to be independent of temperature down to 120 mK before showing a continuous increase with decreasing temperature and saturating below 50 mK. The total increase in ?? is 2 parts in 10^?5. The temperature dependence of ?? mimics the increase in the resonant frequency found in the torsional oscillator studies and also the increase found in the shear modulus measurements.