Session A16: Liquid and Solid Helium

Solid helium in rigid torsional oscillators

In torsional oscillator experiments on solid helium, separating out the effect of shear modulus stiffening is important to measure true non-classical rotational inertia (NCRI). An increase in the shear modulus of solid helium stiffens the oscillator and causes the resonant period to drop thus mimicking NCRI. This effect can be multiplied in a torsional oscillator that is not completely rigid. We have carried out measurements in torsional oscillators specially designed to minimize the shear modulus effect. These oscillators are different from conventional ones in two aspects. Annulus sample spaces are located in the outermost part from rotational axes and all other parts consist of rigid metal. In this design, the resonant period change by loading solid helium is maximized and the effect of shear modulus change is minimized. We found a NCRI fraction on the order of $3 \times 10^{-5}$ in these torsional oscillators.   

Thermal Conductivity of Solid $^{4}$He in Vycor

In addition to non-classcial rotational inertia (NCRI) observed in torsional oscillator (TO), we have carried out thermal conductivity measurement of solid $^{4}$He embedded in porous Vycor glass to search for possible anomaly related to the onset of NCRI. Because of the high thermal conductivity of bulk solid $^{4}$He, it is difficult to resolve any small `extra' thermal conductivity signal due to the onset of supersolidity. However, when it is confined in porous Vycor, the thermal conductivity of solid $^{4}$He is significantly reduced. This makes it easier to single out possible anomaly. Preliminary measurements show a rounded peak in the thermal conductivity near 0.1 K.   

NMR studies of very dilute concentrations of 3He in solid 4He

We compare the results of recent measurements of the nuclear spin-lattice relaxation time ($T_1$) and nuclear spin-spin relaxation time ($T_2$) for very dilute concentrations of $^3$He ($16 \leq x_3 \leq 2000$ ppm) in solid $^4$He with results from previous studies in the temperature range where the relaxation is attributed to the quantum tunneling of $^3$He atoms in the $^4$He lattice. The comparison shows that the results cannot be explained in terms of a unique correlation time and the effects of $^4$He lattice are important.   

Observation of superfluid components in solid $^{4}$He

Neutron scattering demonstrated that localized superfluid components exist at high pressure within solid helium in aerogel [1]. Two sharp phonon-roton spectra 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. 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. The elastic scattering evidenced in addition to the hcp phase also the bcc-phase. both consisting of a small crystallites as a consequence of the confinement. The structural aspect of coexisting hcp and bcc phases in the aerogel matrix seems to be important for the creation of the localized superfluid components.\\[4pt] [1] H. Lauter, E. Krotscheck, E. Kats, A. V. Puchkov, V. V. Lauter, V. Apaja, I. Kalinin, M. Koza, PRL submitted   

Evidence for a BCC to HCP Phase Transition for Solid Helium in Porous Vycor Glass at 100 bar and 800 mK

In 2004, Kim and Chan\footnote{Kim, E. and Chan, M. H. W., Nature 427, 225 (2004).} found evidence that solid helium grown in porous vycor glass exhibited changes in rotational inertia at millikelvin temperatures similar to that observed for superfluids. The nature of this putative supersolid phase is a question of current debate. Subsequent experiments have shown that supersolid behavior depends strongly on crystal quality. For the case of solid helium in vycor, little is known about the crystal quality, or even the crystal phase. In the present work we have performed transmission x-ray diffraction experiments on solid helium in porous vycor glass, over a range of pressures from 1 bar to 162 bar. At pressures up through 96 bar a single peak is observed in the diffraction pattern. At 114 bar and above this peak is observed to split into three peaks. We tentatively identify the low pressure phase as BCC and the high pressure phase as coexistence between BCC and HCP. We interpret the absence of higher order peaks as due to a combination of zero-point motion and defects.   

Simultaneous observation of 10 MHz ultra sound in solid $^4$He contained in torsional oscillator

Kim and Chan[1] were motivated in part by an anomalous ultra sound propagation observed by Ho et al.[2] in solid $^4$He near 200 mK to carry out torsional oscillator(TO) experiments which led to the discovery of supersolid phenomena. We constructed a 270 Hz TO oscillator which incorporated quartz transducers for simultaneously observing 10 MHz longitudinal ultra sound and torsional oscillation of solid $^4$He samples. We are searching for correlation between behaviors in ultra sound propagation and TO response. The length and density of dislocations extracted from ultra sound and the frequency shifts of TO measured in some half a dozen solid $^4$He samples have not shown clear correlation.\\[4pt] [1] E. Kim and M. Chan, Nature \textbf{427}, 225(2004).\\[0pt] [2] P. Ho, I. Bindloss and J. Goodkind, JLTP \textbf{109}, 409(1997).   

More on the shear modulus of solid helium

In experiments on solid $^{4}$He one finds a striking similarity between the response of torsional oscillators and the shear modulus. It has been suggested that in fact the observed increase in the torsional oscillator frequency at low temperature is just a reflection of the stiffening of the solid helium, and thus that of the oscillator as a whole. In some cases this may indeed be the case, but a recent experiment by Keiya Shirahama and Eunseong Kim's groups in which a measurement of the shear modulus was incorporated in a torsional oscillator cell seemed to indicate that the response of the solid to shear is decoupled from that of the oscillator. However, one may object that a) the shear was not applied at a frequency different from that of the oscillator, and that b) the direction of the applied shear was orthogonal to the stress imposed by the motion of the oscillator. In a series of experiments using two stacks of piezoelectric transducers that can be excited, and are able to detect, in orthogonal shear directions, we show that shearing the solid at one frequency affects the shear modulus at different frequencies, and similarly, that shearing in one direction affects the modulus as measured at the orthogonal direction. We conclude that quite generally shear and torsional oscillator responses are decoupled. And while they may both reflect the same underlying physics, it is unlikely that one causes the other.   

Simultaneous Measurement of Non-Classical Rotational Inertia and Shear Modulus of Solid $^{4}$He

A failure to rotate or oscillate is the essential nature of low temperature superfluid helium, and more technically known as non-classical rotational inertia (NCRI). It is counter-intuitive, but NCRI is also found in solid helium-4 below $\sim$200 mK [1,2]. Recently, shear modulus showed unusual increase with striking resemblance to those of NCRI [3]. Extended measurements show the NCRI occurs only in a stiffened Bose solid, but it is not understood how they are related. Here we report the first simultaneous measurement of shear modulus and NCRI in solid helium to elucidate the fundamental connection between them. Both emerge at remarkably similar temperatures, whereas no quantitative agreement between the increase of the shear modulus and the magnitude of NCRI is found. The increase of shear modulus seems to be the necessary condition for the onset of NCRI.\\[4pt] [1] E. Kim and M. H. W. Chan \textit{Nature} \textbf{427}, 225-227 (2004)\\[0pt] [2] E. Kim and M. H. W. Chan \textit{Science} \textbf{305}, 1942 (2004)\\[0pt] [3] J. Day and J. Beamish \textit{Nature} \textbf{450}, 853-856 (2007)   

Interplay of Aerogel Anisotropy and Superfluid $^3$He Textures

The effect of aerogel anisotropy on the $^3$He superfluid order parameter and the relative stability of $A$ and $B$-phases has been investigated. We have performed pulsed NMR on $^3$He in high porosity aerogel samples that have different types of anisotropy, characterized with an optical, cross-polarization technique. One aerogel sample has $14.3\%$ growth-induced axial stretching. Its superfluid phase diagram is occupied by the $A$-phase. Linewidth analysis gives the distribution of the orbital angular momentum, $\vec{l}$. The orientation of $\vec{l}$ is consistent with an easy plane distribution that is perpendicular to the strain axis. A second aerogel sample is axially compressed mechanically by $22.5\%$. The major part of the zero magnetic field phase diagram is occupied by the $B$-phase. Additionally, our results show that aerogel anisotropy introduced by compressing and stretching have different orienting effects on the $^3$He superfluid order parameters. This work was supported by the National Science Foundation, DMR-1103625.   

Experiments with $^{3}$He in 10{\%} uniaxially compressed aerogel: the superfluid phase diagram

Entraining $^{3}$He in aerogel provides a way to introduce disorder in the otherwise ideal quantum fluid. Motivated by the recent prediction that uniaxially compressed aerogel can stabilize the anisotropic A phase over the isotropic B phase, we use a torsional oscillator technique to measure the superfluid phase diagram of $^{3}$He entrained in 10{\%} axially compressed, 98{\%} porous aerogel. We observe that a broad region of the temperature-pressure phase diagram is occupied by the metastable A phase. The reappearance of the A phase on warming from the B phase, before superfluidity is extinguished at T$_{c}$, is in contrast to its absence in uncompressed aerogel. We also find that the anticipated alignment of the angular momentum vector by compression is not observed.   

Application of MEMS Devices to the Study of Liquid $^{3}$He

We report measurements on the mechanical properties of a micro-electro-mechanical (MEMS) resonator submerged in liquid $^{3}$He at millikelvin temperatures and at pressures 3, 21 and 29 bar. The device consists of a pair of parallel plates with a well-defined gap of 0.75 $\mu $m. The sub-micron gap size and geometry of the device gives access to physics in the high Knudsen regime and allows the investigation of surface scattering effects in thin films of quantum fluids. Details of design, fabrication, and operation will be presented along with a study of the damping characteristics of the submerged resonator through a wide range of temperatures spanning from classical fluid to degenerate Fermi liquid. The device shows potential for the use in low temperature experiments and to investigate novel phenomena in quantum fluids at the micro/nano scale such as superfluid $^{3}$He films.   

Partial depinning of dislocation in $^4$He from $^3$He impurities induced by thermal roughening

The mechanism of the roughening induced partial depinning of gliding dislocations from $^3$He impurities is proposed [1] as an alternative to the standard ``boiling off'' scenario [2]. We give a strong argument that $^3$He remains bound to dislocations even at large temperatures due to very long equilibration times. This conjecture is based on two observations: First, the experimental data [2] for shear modulus temperature dependence obtained at very different $^3$He concentrations (1 ppb and 300 ppb) can be, practically, collapsed on each other by a simple rescaling of temperature; Second, both moduli can be fit by the Monte-Carlo simulations data within the assumption that the impurities remain confined to the spatial region occupied by dislocation. Conversely, impurities evaporation violates strongly the data collapse and is absolutely inconsistent with the simulations. We propose that such long equilibration time is due to the very narrow band of $^3$He impuritons [3]. \\[4pt] [1] D.Aleinikava, A.B.Kuklov. arXiv:1110.5884v1;\\[0pt] [2] J. Day and J. Beamish, Nature {\bf 450}, 853 (2007); J. Day,O. Syshchenko, and J.Beamish,Phys. Rev. B {\bf 79}, 214524 (2009);\\[0pt] [3] A.F. Andreev, Sov. Phys. Usp. {\bf 19}, 137 (1976)   

Microscopic Dynamics of Liquid Helium Confined in 1D Nanopores

Recently, Toda et al. performed torsional oscillator and heat capacity measurements on liquid He$^4$ confined within FSM-16. This porous silica glass has 1D pores with a very narrow diameter of $d = $ 2.8 nm. This system is an example of a 1D quantum fluid in the sense that the thermal wavelength $\lambda$ is longer than the pore diameter $d$. Because neutron time-of-flight (ToF) spectroscopy probes elementary excitations, it can be used to study the microscopic dynamics underlying the thermodynamic properties of this 1D quantum liquid. Using the Cold Neutron Chopper Spectrometer (CNCS) at the Spallation Neutron Source (SNS), we performed the first direct measurements of the elementary excitation spectrum of liquid He$^4$ confined in FSM-16. Measurements were performed at full pore at temperatures T = 33, 80, 800, and 1500 mK with an elastic energy resolution of approximately 80 $\mu$eV. We will discuss the temperature $T$ dependence of the static structure factor $S(Q)$, the energies $\hbar\omega$ and line widths $\Gamma$ of the phonon-roton spectrum, and the evidence for 2D layer modes in this system. This research was supported by NIST and employed facilities sponsored by the Scientific User Facilities Division of the US Department of Energy.   

Path-Integral Monte Carlo Simulations of the Ideal Strength of HCP Helium 4

Using path-integral Monte Carlo simulations we assess the ideal strength of solid He-4 in its HCP phase. This fundamental material parameter is defined as the stress necessary to produce irreversible deformation in a defect-free crystal. For this purpose we impose slowly increasing homogeneous deformations to defect-free He-4 crystals and measure the corresponding internal stress state. In this manner, we determine the ideal shear strength in the basal plane as a function of the shear orientation, as well as the tensile and compressive strength perpendicular to this plane. Our results establish upper bounds to the strength of real HCP He-4 crystals.   

Fitting of m*/m with Divergence Curve for He$_{3}$ Fluid Monolayer using Hole-driven Mott Transition

The electron-electron interaction for strongly correlated systems plays an important role in formation of an energy gap in solid. The breakdown of the energy gap is called the Mott metal-insulator transition (MIT) which is different from the Peierls MIT induced by breakdown of electron-phonon interaction generated by change of a periodic lattice. It has been known that the correlated systems are inhomogeneous. In particular, He$_{3}$ fluid monolayer [1] and La$_{1-x}$Sr$_{x}$TiO$_{3}$ [2] are representative strongly correlated systems. Their doping dependence of the effective mass of carrier in metal, m*/m, indicating the magnitude of correlation (Coulomb interaction) between electrons has a divergence behavior. However, the fitting remains unfitted to be explained by a Mott-transition theory with divergence. In the case of He$_{3}$ regarded as the Fermi system with one positive charge (2 electrons + 3 protons), the interaction between He$_{3}$ atoms is regarded as the correlation in strongly correlated system. In this presentation, we introduce a Hole-driven MIT with a divergence near the Mott transition [3] and fit the m*/m curve in He$_{3}$ [1] and La$_{1-x}$Sr$_{x}$TiO$_{3}$ systems with the Hole-driven MIT with m*/m=1/(1-$\rho ^{4})$ where $\rho $ is band filling. Moreover, it is shown that the physical meaning of the effective mass with the divergence is percolation in which m*/m increases with increasing doping concentration, and that the magnitude of m*/m is constant.\\[4pt] [1] Phys. Rev. Lett. 90, 115301 (2003).\\[0pt] [2] Phys. Rev. Lett. 70, 2126 (1993).\\[0pt] [3] Physica C 341-348, 259 (2000); Physica C 460-462, 1076 (2007).