Crystalline Helium Research Articles

Shift and broadening of resonance lines of antiprotonic helium atoms in solid helium

We have estimated the shift and broadening of the resonance lines in the spectrum of antiprotonic helium atoms $\overline{p}{\mathrm{He}}^{+}$ implanted in solid helium $^{4}\mathrm{He}$. The application of the response function for crystalline helium has enabled determination of the contributions from the collective degrees of freedom to the shift and broadening. It occurs that the broadening due to the collective motion is negligible compared to the natural line width. The available pair-correlation functions for crystalline $^{4}\mathrm{He}$ have been applied for estimating the resonance-line shift due to collisions of $\overline{p}{\mathrm{He}}^{+}$ atom with the surrounding $^{4}\mathrm{He}$ atoms. The dependence of the line shift, which has been calculated in the quasistatic limit, on the solid-$^{4}\mathrm{He}$ density is nonlinear.

Solid 4He and the Supersolid Phase: from Theoretical Speculation to the Discovery of a New State of Matter? –A Review of the Past and Present Status of Research–

The possibility of a supersolid state of matter, i.e., a crystalline solid exhibiting superfluid properties, appeared in theoretical studies about forty years ago. After a long period of little interest due to the lack of experimental evidence, it has attracted strong experimental and theoretical attention in the last few years since Kim and Chan (Penn State, USA) reported evidence for nonclassical rotational inertia effects, a typical signature of superfluidity, in samples of solid 4He. Since this first observation, other experimental groups have observed such effects in the response to the rotation of samples of crystalline helium, and it has become clear that the response of the solid is extremely sensitive to growth conditions, annealing processes, and 3He impurities. A peak in the specific heat in the same range of temperatures has been reported as well as anomalies in the elastic behaviour of solid 4He with a strong resemblance to the phenomena revealed by torsional oscillator experiments. Very recently, the observation of unusual mass transport in hcp solid 4He has also been reported, suggesting superflow. From the theoretical point of view, powerful simulation methods have been used to study solid 4He, but the interpretation of the data is still rather difficult; dealing with the question of supersolidity means that one has to face not only the problem of the coexistence of quantum coherence phenomena and crystalline order, exploring the realm of spontaneous symmetry breaking and quantum field theory, but also the problem of the role of disorder, i.e., how defects, such as vacancies, impurities, dislocations, and grain boundaries, participate in the phase transition mechanism.

Motion of charges and singularities in the vacancy spectrum in crystalline helium

The Van Hove singularities in the vacancy spectrum of 4He crystals are manifested as singularities in the field dependence of the drift velocity of charges. In 3He, the field dependence of the drift velocity is determined by the vacancy spectrum in the completely spin-polarized state of the crystal.

Inelastic X-ray spectroscopy with high energy resolution under high pressures

X-ray scattering experiments with energy resolutions in the range of several meVs open new possibilities for the study of the dynamics in condensed matter under high pressures. A special beryllium pressure cell was used in our investigations of liquid and solidified single crystalline helium at 58 MPa. The dynamical excitations could be clearly identified. Another type of pressure cell, the Paris-Edinburgh cell, allowed the observation of longitudinal phonons of silicon under a pressure of 4 GPa.

Epitaxial Y1Ba2Cu3O7−y/Y1−xPrxBa2Cu3O7−y heterostructures

For a variety of device applications, junction devices in particular, we have demonstrated a heterostructure system of Y1Ba2Cu3O7−y/Y1−xPrxBa2Cu3O7−y which maintains epitaxy over the entire Pr composition range x=0–1. We have grown both trilayer and multiperiod superlattices which show nearly single crystalline helium ion backscattering minimum yields of <6% in the topmost layer. X-ray diffraction measurements indicate c-axis orientation by a transverse scan across (005) line with a full width at half maximum of 0.6° and 0.4° on MgO and SrTiO3 substrates, respectively. Scanning Auger electron depth profiles and cross-sectional transmission electron micrographs indicate abrupt Pr/Y interfaces within one unit cell and virtually no disruption of the layered structure at the interface. These results indicate the potential for the growth of excellent heterostructures and superlattices of the high-temperature superconductors.

Quantum crystal with jumps of particles

The relation between quasi-averages and averages in the case of spontaneous breakdown of translational symmetry is analysed. A hybrid system with virtual breakdown and restoration of translational symmetry is examined. The definitions of phase probabilities and phase transitions are given. The probabilities of the formation of the localized and nonlocalized phases are found and the existence of solid-liquid phase transition is proved. The calculated melting temperatures of the crystals of the inert group are in good agreement with experimental data. The collective excitation spectrum of the hybrid crystal is determined. An explanation of the high temperature anomaly of the specific heat in crystalline helium is proposed.

Cryostat for accurate x-ray diffractometry of crystalline helium to 60 mK and 25 MPa

A cryostat designed for accurate x-ray diffractometry of crystalline helium and other solidified gases is described and its performance characterized. The cryostat is a rigid tail design. It holds the crystal, grown at pressures up to 25 MPa, in fixed orientation and position independent of the levels of the cryogenic fluids. Such stability is necessary for crystal growth, orientation, characterization, and measurements of x-ray reflection intensities and x-ray scattering. A combination of beryllium and aluminized Mylar x-ray windows permits x-ray access to the specimen crystal over broad angular ranges, essentially 360° in polar angle and ±40° in inclination. At the same time, thermal radiation is small enough to permit temperatures as low as 60 mK to be achieved with a simple dilution refrigerator.

Measurements of the charge-carrier mobility in crystalline helium

Measurements of the charge-carrier mobility in crystalline helium

Generalized cluster expansions

A unified approach to the cluster expansion of the ground-state energy of a system whose wave function is a product of two factors, one of which is a Jastrow function, is presented. It is shown that several previously derived expansions, notably those of Wu and Feenberg and of Massey and Woo, are special cases of this one. The most general case of this expansion, when applied to crystalline helium, incorporates “self-consistent” phonons, exchange, and the Massey-Woo treatment of short-range correlations.

Calculation of Phonon Frequencies and Thermodynamic Properties of Crystalline bcc Helium

The lattice dynamics of crystalline bcc helium is treated by using the time-dependent Hartree approximation together with the results of variational calculations of the ground-state energy using correlated trial wave functions. The phonon spectrum has been calculated for various densities of bcc ${\mathrm{He}}^{3}$ and ${\mathrm{He}}^{4}$. We present dispersion curves, density-of-states histograms, and sound velocities for selected densities. In addition we have calculated (for these densities) the mean-square displacement and the specific heat ${C}_{V}$ which is expressed as a temperature-dependent Debye temperature $\ensuremath{\Theta}(T)$. It is found that the reduced $\ensuremath{\Theta}\ensuremath{-}T$ relationships follow a universal curve for all densities considered. This is a theoretical confirmation of the experimental fact that the bcc phase of crystalline helium (like the other crystalline phases of ${\mathrm{He}}^{3}$ and ${\mathrm{He}}^{4}$) shows a thermodynamic behavior very similar to that of ordinary crystals. The calculated Debye temperatures are about 15-20% higher than those recently measured by Sample and Swenson. A possible cause for this discrepancy is indicated.

Green's function approach to the quantum many-body theory of the solid state

TheGreen's function approach is used to develop a quantum many-body theory of the solid state which should work at low temperatures as well as in the neighbourhood of phase transition points. The theory is applicable also in those cases where the traditional expansion of the potential in powers of the atomic displacements is entirely inadequate (crystalline helium). The starting point of our approach is the concept of broken symmetry since the invariance of the equilibrium ensemble under the continuous group of infinitesimal translations is reduced in a crystalline solid to the invariance under finite translations through a lattice vector. A homogeneous integral equation is derived which has nontrivial solutions in the crystalline state. By this equation it is shown that the umklapp phonons are the symmetry restoring collective modes expected due to a general theorem ofGoldstone. The single particle excitations and the structure of the Dyson mass operator in the crystalline state are discussed. It is further shown that the homogeneous Bethe-Salpeter equation for the linear response to an external disturbance possesses symmetry breaking solutions which are connected to the lattice dynamics of the solid state. These collective excitations (phonons) are exhibited in RPA and tight-binding approximation for monoatomic cubic crystals with a Bravais lattice in order to demonstrate how the present theory reproduces well-known results.

Theory of Quantum Crystals. II. Three-Body Term in the Cluster Expansion

In a previous paper, denoted as I, the ground-state properties of crystalline helium were studied by a variational method which used a cluster expansion evaluation of the energy, ${E}_{0}$. The basic approximation of that work was the truncation of the cluster expansion after the one- and two-particle terms, ${E}_{01}+{E}_{02}$. We have tested this approximation by numerical computation of the three-body term, ${E}_{03}$, of the expansion. Using the analytic form of the trial wave function given in I, we find, for bcc $^{3}\mathrm{He}$, that ${E}_{03}\ensuremath{\approx}{10}^{\ensuremath{-}2}{E}_{02}$ at the minimum in ${E}_{01}+{E}_{02}$. Furthermore, when ${E}_{03}$ is included in the variations, ${E}_{03}$ remains small and the minimum energy is essentially unchanged, but the values of the wave-function parameters are improved somewhat. These results indicate that the cluster expansion is converging rapidly. The computations are performed as a function of density, and improved results for the ground-state pressure, compressibility, sound velocities, and exchange integral are also presented. Similar calculations at a single density in hcp $^{3}\mathrm{He}$ and $^{4}\mathrm{He}$ show that the close packing causes ${E}_{03}$ to be larger; however, it is still only $\frac{1}{20}$ the value of ${E}_{02}$, and the truncation of the cluster expansion is probably valid here as well. It is shown that the rate of convergence of the cluster expansion depends on the form of the trial function. A numerical example is given of a form for which the approximation of I breaks down. A critique of the expansion of Brueckner and Frohberg is given. On a basis of a numerical test, it is found that they have neglected an important term in truncating their expansion, so that the validity of their variational procedure is uncertain. Some possible improvements in the theory, such as solving a differential equation for the correlation function and including the effects of the phonon spectrum, are discussed. Details of our method of evaluating the three-body terms are given in two Appendices.

Calculations of Sound Velocities in Crystalline Helium at Zero Temperature

Calculations of Sound Velocities in Crystalline Helium at Zero Temperature

Calculations of Sound Velocities in Crystalline Helium at Zero Temperature

Calculations of Sound Velocities in Crystalline Helium at Zero Temperature