Supersolidity and Disorder in Solid Helium 4

Supersolidity is a rather controversial issue which has been revived recently by a number of torsional oscillator (ac-rotation) experiments with solid helium 4. One possibility would be that the ground state of helium 4 crystals contains a Bose-Einstein condensate of mobile vacancies. However, the supersolid signal was shown to depend on sample history. In addition, dc-flow experiments show that superfluid transport of mass does not occur in solid helium, except if it contains appropriate grain boundaries. As a consequence, we believe that supersolidity is not an intrinsic property of helium single crystals, but that it is due to quenched disorder. We report experiments on pressure relaxation in and light scattering from solid samples, that give additional evidence for the existence of disorder in helium crystals. We also describe our recent study of the wetting properties of grain boundaries.      

Supersolidity and the Thermodynamics of Solid Helium

The specific heat of solid helium in the temperature range below about 1.2 K has been found to contain a term varying as T ⁷, in addition to the usual T ³ contribution always found in a crystalline dielectric solid. It has been proposed by Anderson, Brinkman and Huse, (Science 310, 1164 (2005)) that the existence of this T ⁷ term supports their theory of supersolidity. However, in this paper we show that corrections to the phonon specific heat arising from phonon dispersion are much larger than expected based on simple order of magnitude estimates and, as a consequence, it is very unlikely that the existence of this T ⁷ term can be considered as evidence for supersolidity.      

Optical Observations of Disorder in Solid Helium 4

It has been proposed that the supersolidity of helium 4 is associated with disorder in the solid samples. We report optical observations of this disorder in samples grown by different methods. We show that, when grown by the “blocked capillary method” as in most experiments showing anomalous phenomena, solid helium 4 can be polycrystalline with grain sizes down to the micrometer range, much smaller than the 0.1 mm found in some other experiments. We analyze the properties of grain boundaries, and in particular the existence of liquid channels at the contact of grain boundaries with walls. Our analysis includes measurements of the contact angle of the liquid-solid interface with these walls, which exhibits a large hysteresis. Furthermore, we predict that similar channels should exist at the junction between grain boundaries.     

Flow and Supersolidity in Helium

Recent torsional oscillator measurements showed evidence of non-classical rotational inertia in solid helium at temperatures below 200 mK and generated a great deal of interest in a possible supersolid state. The nature and properties of such a state are still unclear, although experiments involving ³He impurities and crystal annealing may provide clues. It would be very interesting to know whether supersolids share any of the other unusual properties of superfluids: superleaks, persistent currents, second sound and quantized vortices. We have studied the response of solid helium to pressure differences, in order to look for unusual flow properties that might be associated with supersolidity. Our measurements involved both helium confined in the nanometer pores of Vycor glass and bulk solid helium, at temperatures as low as 30 mK. Near melting, solid helium flows very easily but we did not see any evidence of superflow at low temperatures. If helium does become a supersolid at low temperatures, then its response to pressure gradients must be very different from that of liquid helium. We describe these and other experiments and discuss the role that defects may play in the low temperature behavior of solid helium.     

Overview on Solid 4He and the Issue of Supersolidity

Here we provide an overview of the status of the field of solid ⁴He with a focus on the recent theoretical and experimental activities stimulated by the 2004 experiments of Kim and Chan. The overview attempts to place the experimental and theoretical work in context, to respect the historical flow of the field and discuss our present understanding of the question of supersolidity in ⁴He. The possibility of supersolidity in cold atoms and in other systems is also addressed. Special issues of the Journal of Low Temperature Physics (168(3/4), 2012; 169(3/4), 2012), in addition to this issue, have been devoted to this subject and this overview is meant to accompany those issues of the journal.     

Temperature Independent Nucleation of Solid Helium 4 Below 1K

Nucleation of solid helium in superfluid helium was studied in a temperature range between 50mK and 1K. Pulsed electrostatical compression was employed to initiate nucleation in a slightly overpressurized superfluid helium. The nucleation rate w was estimated from a distribution of the overpressure P _eff required for nucleation. The temperature dependence of P _eff at constant was essentially flat between 50mK and 1K. The ln was almost linear in P _eff within the resolution of our data.     

On the Nature of Disorder in Solid 4He

We apply a modified Debye approach to calculate the Gibbs free energy for different structural phases and crystallite sizes in ⁴He. Atoms are assumed to interact via the Aziz potential. We have found that some intermediate (between hcp and bcc) phase predicted previously is more favorable than hcp at low temperatures and for small sizes. We show that it can exist in a wide pressure range up to 60 bar in ⁴He for crystallite sizes about 3,000 atoms. For larger sizes (10,000 atoms or more) this phase becomes unfavorable. In multidomain structures the intermediate phase competes with hcp and metastable fcc that can be a reason for disorder in solid ⁴He.     

Growth Rate of Frost Heave in Helium and Mass Transport in Solid 4He

Frost heave phenomena have been studied in ⁴He on porous vycor glass, in which ⁴He in the pores remained supercooled fluid below the bulk melting temperature, T _m . When we cool a bulk solid at T below T _m on the vycor, the bulk solid sucks the supercooled liquid in the pores and grows. We measured the maximum frost heave pressure over bulk melting pressure, P _m , as a function of ΔT=T _m −T. When temperature was suddenly lowered, the frost heave pressure increased in time to a next equilibrium pressure and we measured the time constant and derived the frost heave rate. The frost heave rate was measured as a function of temperature and decreased very rapidly as temperature was lowered. We propose models to explain the mass transport in solid either by vacancy or by amorphous solid between bulk solid ⁴He and vycor. From measured temperature dependence of the rate in comparison with our model, we conclude the frost heave rate is determined by mass flow in solid ⁴He due to thermally-activated vacancy diffusion.      

Density Functional Theory of the Interface between Solid and Superfluid Helium 4

No Heading We report a calculation of the equilibrium profile of the interface between superfluid helium 4 and its solid phase at 0 K. To calculate the excess energy of the interface, we use the density functional theory that allowed us to obtain the equilibrium density of both phases. We compare our result to the experimental and to a previous microscopic calculation.PACS numbers: 68.08.–p, 67.80.–s, 67.40.Kh.     

Acoustic Nucleation of Solid Helium 4 on a Clean Glass Plate

We have used a focused acoustic wave to nucleate solid helium 4 on a clean glass plate. From the reflectance of light at the glass/helium interface, we measured the amplitude of the acoustic wave in the focal region. Nucleation was found to be stochastic, occurring 4.3±0.2 bar above the equilibrium melting pressure. This overpressure is 2 to 3 orders of magnitude larger than found in previous nucleation studies where favorable defects or impurities must have been present. From the statistics of nucleation and its temperature dependence above 300 mK, we have estimated the activation energy E for the nucleation on the glass plate; we have found E/k _B T=10. This value is consistent with a thermally activated nucleation on a single site at the glass/helium interface. We also found a crossover to a quantum nucleation regime below 300 mK. We focally discuss some implications of these results for the homogeneous nucleation of solid helium and the search of a liquidsolid spinodal limit.     

Nonlinear Space-Charge-Limited Ion Currents in Solid Helium

Expressions are obtained for steady-state and transient space-charge-limited currents for a nonlinear velocity-field relation of the form v(E) = (/) × sinh(E). Our experimental results are analyzed with these expressions. The positive-ion diffusion coefficient is a tensor with two activation energies associated with motion along c axis and in the basal plane. For bcc ³ He the dependence of negative-ion velocity on field is highly nonlinear and temperature dependent. Results are compared with those of other authors and discussed in light of different models for ionic motion in solid helium. The diffusion coefficients for positive ions and isotopic impurities are compared and discussed.     

Search for Supersolidity in 4He in Low-Frequency Sound Experiments

We present results of the search for supersolid ⁴He using low-frequency, low-level mechanical excitation of a solid sample grown and cooled at fixed volume. We have observed low frequency non-linear resonances that constitute anomalous features. These features, which appear below ∼0.8 K, are absent in ³He. The frequency, the amplitude at which the nonlinearity sets in, and the upper temperature limit of existence of these resonances depend markedly on the sample history.     

Quantum Nature of Dislocations in Pure bcc Helium

Recent experiments show the thermal growth of dislocation lines in ultra-pure bcc ³He. The activation energy for the growth of the dislocation lines is found to agree with the activation energy of mass diffusion. We propose that these dislocations are topological defects in the phase of the complex order-parameter, which describes the dynamic zero-point atomic correlations, unique to the bcc phase. There is also a shear field associated with these topological defects. We show that the smallest topological defect is a localized excitation, a loop-defect, which leads to the exponential growth of the dislocation lines with temperature.     

Experimental Study of Classical and Quantum Internal Friction in Solid 4He

We measured the dissipation resulting from internal friction in hcp solid ⁴He at temperatures between 0.8 K and 2.5 K. Solid ⁴He is contained inside an annular metal cell forming a part of a torsional oscillator. An oscillatory motion of the cell walls applies shear stress on the solid ⁴He. The resulting shear strain within the solid ⁴He generates dissipation because of the internal friction. The experimental sensitivity was high enough to detect dissipation caused by internal friction associated with elementary excitations of the solid. At temperatures below 1.6 K, internal friction is associated with diffusion of single point defects responsible for the climb of dislocations. At higher temperatures, the main mechanism of internal friction appears to be associated with phonon exchange between parts of the solid moving relative to each other under the applied shear stress. This particular dissipative mechanism was called “quantum phonon friction” [Popov in Phys. Rev. Lett. 83:1632–1635, 1999]. The physical mechanism associated with this type of friction involves an irreversible transfer of momentum from the phonons to the lattice via an Umklapp process. Our data are in a very good agreement with this model.

     

Vortex Pinning to a Solid Sphere in Helium II

We report here the results of a computer simulation of quantized vortex pinning in He II at 0 K in the simple situation where a single sphere and a rectilinear vortex are considered. Our simulation shows that a vortex nearby a sphere is captured due to a velocity field produced by the sphere, exciting Kelvin waves. The dependence of the “pinning” on temperature is investigated as well. Finally, the possibility of pinning in PIV experiments, which visualize superfluid turbulence, is discussed.     

Tunneling Defect Nanoclusters in hcp 4He Crystals: Alternative to Supersolidity

A?simple model based on the concept of resonant tunneling clusters of lattice defects is used to explain the low temperature anomalies of hcp ⁴He crystals (mass decoupling from a torsional oscillator, shear modulus anomaly, dissipation peaks, heat capacity peak). Mass decoupling is a result of an internal Josephson effect: mass supercurrent inside phase coherent tunneling clusters. Quantitative results are in reasonable agreement with experiments.     

Experimental Apparatus to Search for Supersolidity in Monolayer ^4He on Graphite

We describe some details of a new experimental setup for torsional oscillator (TO) measurement of $^4$ He monolayers adsorbed on a graphite surface. This setup is designed to seek for the possible supersolid phase, in which crystalline order coexists with superfluidity, in two dimensional (2D) solid $^4$ He below 300 mK. Among such 2D solids, the commensurate phase in the second layer on graphite is the most hopeful candidate for the novel supersolid phase since it is the lowest-density quantum solid ever found. An exfoliated graphite substrate we used is ZYX which has at least ten times longer surface coherence length compared to Grafoil, an exfoliated graphite most commonly used in previous experiments. The first version of TO we made has the resonant frequency of 786.8 Hz and the Q value of $1.1\times 10^5$ at $T \le 10$  mK. The resonant frequency of this particular TO without any He samples ( $f_{\mathrm {cell}}$ ) showed unexpectedly large temperature variation and non-reproducibility below 1 K as well as sudden jumps when mechanical shocks are applied to the experimental apparatus. We found the stability of $f_{\mathrm {cell}}$ is highly correlated with the temperature stability of 1 K pot in dilution refrigerator.