Solid Helium Research Articles

Strength of solid helium under high pressure

Helium is commonly used as a pressure transmitting medium to render the sample pressure hydrostatic in high pressure experiments with diamond anvil cells. On solidification under pressure helium begins to develop strength that is characteristic of any solid. The estimation of the compressive strength of helium as a function of pressure is important as it helps in estimating the nonhydrostatic stresses that can develop in the sample even when it remains immersed in helium pressure transmitting medium. The x-ray diffraction data on polycrystalline samples obtained with the radial diffraction geometry are commonly used to determine the compressive strength of solids. This method fails in the case of helium because of it s low scattering power. The nonhydrostatic stresses that develop in crystalline solids immersed in helium pressure transmitting medium were used to estimate the strength of helium. The diffraction data available in the literature were selected for this study. It was important for this study to consider the data from the experiments that were conducted ensuring that the samples did not come in contact with the anvils. The analysis of these data suggests that the strength of helium remains low (< 0. 1 GPa) at pressures below 20 GPa and increases to ∼2 GPa at 100 GPa.

NMR Study of Disordered Inclusions in the Quenched Solid Helium

Phase structure of rapidly quenched solid helium samples is studied by the NMR technique. The pulse NMR method is used for measurements of spin-lattice $T_1$ and spin-spin $T_2$ relaxation times and spin diffusion coefficient $D$ for all coexisting phases. It was found that quenched samples are two-phase systems consisting of the hcp matrix and some inclusions which are characterized by $D$ and $T_2$ values close to those in liquid phase. Such liquid-like inclusions undergo a spontaneous transition to a new state with anomalously short $T_2$ times. It is found that inclusions observed in both the states disappear on careful annealing near the melting curve. It is assumed that the liquid-like inclusions transform into a new state - a glass or a crystal with a large number of dislocations. These disordered inclusions may be responsible for the anomalous phenomena observed in supersolid region.

Features of the temperature dependence of pressure of solid helium at low temperatures

A series of experiments has been performed to investigate the conditions of formation of a disordered (glass-like) state in crystals of 3He. With the help of precise measurements of pressure at constant volume it has been established that a glass phase is formed easily in rapidly cooled crystals grown under homogeneous temperature conditions in the presence of large numbers of nucleation centers. This phase can be removed only by careful annealing. This result has been found in both 3He and 4He, and is independent of type of quantum statistics and determined mainly by crystal growth conditions. An analysis of similar measurements has been performed using a different cell where during the crystal growth a directed temperature gradient was created. In this case, additional defects created as a result of deformation of the crystal were necessary to form a glass-like phase. The degree of deformation of a crystal, achievable in the experiment, was sufficient to form a glass-like phase in solid 4He, but not in a crystal of 3He where the atoms have a large amplitude of zero-point oscillations. Analyzing a temperature dependence of pressure, a study of the features of a phonon contribution to the pressure was also carried out. It was found that in both crystals 3He and 4He at different thicknesses of samples the phonon pressure differs by several times. This effect is qualitatively explained by that that in thin samples an interaction among layers of atoms becomes stronger. This leads to decreasing the phonon contribution to the thermodynamic properties of the helium crystal at low temperatures.

Elastic and Acoustic Measurements in Solid 4He

We describe results of elastic and acoustic measurements in solid helium in the range of parameters where supersolidity is observed. A variety of polycrystalline and mono-crystalline samples has been studied. We observed a decrease with temperature of the uniaxial compression modulus in a polycrystalline sample by up to 25 %. Such softening is usually explained in term of decrease of base-plane shear modulus, c 44, of hcp 4He solid. Our results translates into a decrease of c 44 of the constituent crystallites between 77 % and 82 %, depending on the model. In the acoustic measurements, we attempted to check whether the description of softening via c 44 is appropriate by fitting frequencies of observed resonances to numerical calculations. Neither the measured positions, nor the line shapes of the resonances fit the simulations at low temperatures, indicating that an alternative approach is required.

Colloquium: Supersolids: What and where are they?

The ongoing experimental and theoretical effort aimed at understanding nonclassical rotational inertia in solid helium has sparked renewed interest in the supersolid phase of matter, its microscopic origin and character, and its experimental detection. The purpose of this Colloquium is to provide a general theoretical framework for the phenomenon of supersolidity, review some of the experimental evidence for solid $^{4}\mathrm{He}$, and discuss its possible interpretation in terms of physical effects underlain by extended defects (such as dislocations). Quantitative support to our theoretical scenarios by means of first-principle numerical simulations is provided. Alternate avenues for the observation of the supersolid phase, not involving helium but rather assemblies of ultracold atoms, are also discussed.

Reprise of First Experiment Casts Doubt on Supersolid Helium

A second pair of physicists has found further evidence that solid helium doesn't flow—ironically, by tweaking the experiment that started the controversy in the first place.

Elastic effects in torsional oscillators containing solid helium

A number of recent experiments have used torsional oscillators to study the behavior of solid helium. The oscillator frequencies increased at temperatures below 200 mK, an effect attributed to decoupling of a fraction of the helium mass---the signature of a ``supersolid'' phase. However, helium's shear modulus also increases below 200 mK and the frequency of a torsional oscillator depends on its elastic properties, as well as on its inertia. In many experiments helium is introduced via a hole in the torsion rod, where its shear modulus contributes to the stiffness of the rod. In oscillators with relatively large torsion rod holes, changes in the helium's shear modulus could produce the entire low temperature frequency shifts that have been interpreted as mass decoupling. For these oscillators we also find that the known elastic properties of helium in the torsion rod can explain the observed TO amplitude dependence (which has been interpreted as a critical velocity) and the TO dissipation peak. However, in other oscillators these elastic effects are small and the observed frequency changes must have a different origin.

Possible frictionless transport of amorphous matter in confined microdomains

Almost frictionless transport of amorphous (polymeric) matter in confined microdomains at room temperature regime is investigated by using the verified transition-rate approach which has been successfully adopted to study the critical transport of amorphous solid helium in confined environment. The critical temperatures related to the nearly frictionless transport of polymeric fluids were found after selecting specific activation energies.

Disorder, Supersolidity, and Quantum Plasticity in Solid Helium 4

Abstract Several years after Kim and Chan’s discovery of an anomaly in the ro-tation properties of solid helium (Kim and Chan in Nature 427:225, 2004; Science305:1941, 2004), the interpretation of the observed phenomena as a manifestationof supersolidity remains controversial. J. Beamish and his collaborators have shownthat the rotation anomaly is accompanied by an elastic anomaly (Day and Beamish inNature 450:853, 2007; Day et al. in Phys. Rev. Lett. 104:075302, 2010; Syshchenkoet al. in Phys. Rev. Lett. 104:195301, 2010): when the rotational inertia apparentlyincreases, the shear modulus decreases. This softening is due to the appearance, in thesolid, of a large reversible plasticity that is a consequence of the evaporation of 3 Heimpurities from dislocations that become mobile. This plasticity is called “quantumplasticity” because the dislocations move by quantum tunneling in the low tempera-ture limit.Since the main evidence for supersolidity comes from torsional oscillator (TO)experiments, and since the TO period depends on both the inertia and the stiffnessof solid

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.

Measurements of the Dielectric Constant of Solid Helium at Low Temperatures

A careful measurement of the dielectric constant of solid 4He was made to search for signatures associated with the reported onset of nonclassical rotational inertia and shear modulus stiffening. The samples studied include zero-pressure liquid, solid-liquid mixtures on the melting-curve and solid helium. It was found that the dielectric constant of solid 4He decreases smoothly with temperature below 300 mK, showing no measurable anomalies down to 50 mK. The new measurements do not show the anomalous upturn effect that was reported in our previous measurements.

4He crystal quality and rotational response in a transparent torsional oscillator

We have studied natural purity $^{4}$He single crystals and polycrystals between 10 and 600 mK using a torsional oscillator with a 2 cm$^{3}$ rigid cell made of sapphire with a smooth geometry. As the temperature was lowered, we observed sample dependent but reproducible resonant frequency shifts that could be attributed to a supersolid fraction of order 0.1%. However, these shifts were observed with single crystals, not with polycrystals. Our results indicate that, in our case, the rotational anomaly of solid helium is more likely due to a change in stiffness than to supersolidity. This interpretation would presumably require gliding of dislocations in more directions than previously thought.

Interpreting Torsional Oscillator Measurements: Effect of Shear Modulus and Supersolidity

The torsional oscillator is the chief instrument for investigating supersolidity in solid 4He. These oscillators can be sensitive to the elastic properties of the solid helium, which show anomalies over the same range of temperature in which the supersolid phenomenon appears. In this report we present a detailed study of the influence of the elastic properties of the solid on the periods of torsional oscillators for the various designs that have been commonly employed in supersolid measurements. We show how to design an oscillator which measures supersolidity, and how to design one which predominantly measures elasticity. We describe the use of multiple frequency TOs for the separation of the elastic and supersolid phenomena.

Shear modulus of an elastic solid under external pressure as a function of temperature: The case of helium

The energy of a dislocation loop in a continuum elastic solid under pressure is considered within the framework of classical mechanics. For a circular loop, this is a function with a maximum at pressures that are well within reach of experimental conditions for solid helium suggesting, in this case, that dislocation loops can be generated by a pressure-assisted thermally activated process. It is also pointed out that pinned dislocations segments can alter the shear response of solid helium, by an amount consistent with current measurements, without any unpinning.

Probing phase coherence in solid helium using torsional oscillators of different path lengths

Long-range phase coherence is a critical signature of macroscopic quantum phenomena. To date, nonclassical rotational inertia (NCRI) of solid helium has been reported only in samples with physical dimension of at most 5 cm. We have investigated solid helium in longer path-length torsional oscillators. Samples of length ranging from 6 to 100 cm were grown inside toroids and in self-connected long capillaries. NCRI of $4\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}5}$ and $3\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}5}$ were found in cells with path length of 6 and 9 cm. In cells with path length of 30 and 100 cm, NCRI, if it exists, is less than $7\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}5}$ and $4\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}5}$, respectively.

Elastic constants of solid4He under pressure: Diffusion Monte Carlo study

We study the elasticity of perfect 4He at zero-temperature using the diffusion Monte Carlo method and a realistic semi-empirical pairwise potential to describe the He-He interactions. Specifically, we calculate the value of the elastic constants of hcp helium C_{ij} as a function of pressure up to 110 bar. It is found that the pressure dependence of all five non-zero C_{ij} is linear and we provide accurate parametrization of each of them. Our elastic constants results are compared to previous variational calculations and low-temperature measurements and in general notably good agreement is found among them. Furthermore, we report T = 0 results for the Gruneisen parameters, sound velocities and Debye temperature of hcp 4He. This work represents the first of a series of computational studies aimed at thoroughly characterizing the response of solid helium to external stress-strain.

Studies of Condensed Matter at Low Temperatures by Ultrasonic and other Mechanical Spectroscopies

In the second half of the twentieth century and in the first decade of the twenty first century, many new phenomena came to light in the fields of condensed matter and of materials properties’ at low temperatures. A few examples of these phenomena are: the plasticity and the behavior of dislocations in solid helium-4 (a quantum solid), “high” temperature superconductivity, occurrence of superfluid flow in solid helium (“supersolid”), and, Bose-Einstein condensation of cold atoms. In this presentation descriptions and some discussions are given on the role played in these studies by ultrasonic and other forms of mechanical spectroscopy.

Observation of a Superfluid Component within Solid Helium

We demonstrate by neutron scattering that a localized superfluid component exists at high pressures within solid helium in aerogel. Its existence is deduced from the observation of two sharp phonon-roton spectra which are clearly distinguishable from modes in bulk superfluid helium. These roton excitations exhibit different roton gap parameters than the roton observed in the bulk fluid at freezing pressure. One of the roton modes disappears after annealing the samples. Comparison with theoretical calculations suggests that the model that reproduces the observed data best is that of superfluid double layers within the solid and at the helium-substrate interface.

Laser ablation and spectroscopy of copper in liquid and solid4He

We present an experimental study of the laser-induced fluorescence spectra of Cu atoms in bulk liquid and solid helium matrices as well as in the dense plasma created by the laser ablation of copper in liquid helium. We observe transitions of the valence electron and of inner-shell electrons. The former produce structureless line shapes, a large broadening, and a blueshift. The latter practically are not shifted with respect to the free atom and possess a substructure consisting of a zero-phonon line and phonon wings. We suggest a qualitative interpretation of the observed spectra based on the atomic bubble model that takes the lifting of the $|{M}_{J}|$ degeneracy due to the bubble deformation and matrix-phonon interactions into account.

The role of glassy dynamics in the anomaly of the dielectric function of solid helium

We propose that the acousto-optical (electro-elastic) coupling of the electric field to strain fields localized around defects in disordered 4He causes an increase of the dielectric function with decreasing temperature due to the arrested dynamics of defect excitations. A distribution of such low-energy excitations can be described within the framework of a glass susceptibility of a small volume fraction inside solid 4He. Upon lowering the temperature the relaxation time τ(T) of defects increases and an anomaly occurs in the dielectric function ϵ(ω,T) when ωτ(T) ∼ 1. Since ϵ(ω,T) satisfies the Kramers–Kronig relation, we predict an accompanying peak in the imaginary part of ϵ(ω,T) at the same temperature that the largest change in amplitude occurs at a fixed frequency. We also discuss recent measurements of the amplitude of the dynamic dielectric function that indicate a low-temperature anomaly similar to that seen in the resonance frequency of the torsional oscillator and shear modulus experiments.