Session P17: Quantum Fluids and Solids I

Simulating the Melting Transition of Helium in Two Dimensions

We study the melting behavior of $^4$He in two dimensions with the path integral Monte Carlo method. Systems of helium atoms are simulated in a periodic cell designed to accommodate a triangular solid. We calculate the translational and orientational order parameters, as well as the defect fraction. Defects are defined as atoms with more or less than six neighbors; the nearest neighbor network is found through Delaunay triangulation. Two dimensional melting is a defect-mediated phase transition, thus, defects will proliferate as the solid is melted. Additionally, melting is expected to occur via a two-stage process, with transitions for both translational and orientational order. At high number density (0.0846 \AA$^{-2}$), we have seen a single transition (within the accuracy of our simulations). We are currently working to observe the melting transition at lower densities.   

Lithium, magnesium and sodium $^{4}$He adsorption experiments performed below 1K.

We have constructed a $^{3}$He optical cryostat and used a previously developed technique of Cryogenic Pulsed Laser Deposition(CPLD) $^{(1)}$, to deposit films of sodium, lithium and magnesium onto the surfaces of quartz crystal microbalances at cryogenic temperatures. The elements in the first and second column of the periodic table interact weakly with adsorbed helium. Theoretical calculations predict that helium will wet all the elements lighter than rubidium, but solid-like layers will not form, so liquid and superfluid films can exist at sub-monolayer coverage. We will present vapor pressure isotherms on Li, Mg and Na substrates in the temperature range 0.5K -1.3K and discuss the wetting and superfluid onset behavior. We will also present in-situ optical work function measurements of the metallic films, and discuss the relation between work function and wettability. $^{(1)}$ E. Van Cleve, P. Taborek, J.E. Rutledge JLTP online   

Third Sound Propagation in Superfluid $^4$He Films Adsorbed on Carbon Nanotube Bundles

We have observed the propagation of third sound waves in thin superfluid $^4$He films adsorbed on carbon nanotube bundles. The nanotubes are sprayed onto a plexiglass substrate, forming a tangle of interconnected bundles that is about 15 $\mu$m thick and 2.5 cm square, with an average bundle diameter of about 4 nm. A heater and bolometer at opposite corners allow detection of resonant third sound modes, and the third sound speed is deduced from the resonant frequencies. The helium adsorption is greatly affected by the surface tension forces generated by the high curvature of the nanotubes, and the film thickness on the tubes remains very thin compared to the thickness in flat regions of the cell. As helium is metered into the cell at 1.3 K the Kosterlitz-Thouless transition on the nanotubes is observed as the onset of the third sound signal, and then with increasing film thickness the third sound velocity decreases. The velocity appears to be dropping towards zero at a finite value of the film thickness on the tubes, in qualitative agreement with a surface-tension instability predicted for cylindrical geometries by Cole and Saam [Phys. Rev. Lett., \textbf{32}, 985 (1974)].   

Bose-Einstein Coherence in Two Dimensional Superfluid $^4$He

We present high-resolution measurements of the momentum distribution of atoms in liquid $^4$He films adsorbed in nanoporous MCM-41, with 45 {\AA} mean pore diameter. The measurements were performed at temperatures $T=0.3$ K and $T=2.3$ K and saturated vapor pressure (SVP) in the wavevectors range $24\le Q\le 29$ {\AA$^{-1}$} using the MARI time-of-flight (TOF) chopper spectrometer at the ISIS spallation neutron source. The main goal is to determine whether there is a Bose-Einstein condensate (or coherence) in a finite-size two dimensional (2D) Bose fluid at low temperatures. It is also to investigate the 2D-3D dimensional crossover in the condensate proprieties. We find clear evidence of a condensate parameter, $n_0$, at $T=0.3$ K in the films investigated. In the thinnest film ($\sim$ approximately one atomic layer thick), the observed condensate fraction is greater than but consistent with the bulk superfluid 4he value of 7.25\% within precision; i.e. $n_0=(9.34\pm3.84)$\%. As more $^4$He is adsorbed in the substrate pores, $n_0$ appears to decrease below the bulk value, possibly due to the disorder introduced by the confining media; i.e. $n_0=(2.45\pm2.54)$ \% near full pore filling.   

Dynamics of one and two dimensional solid $^4$He adsorbed on nanotubes

In a previous experiment[1], we showed that one dimensional (1D) solid helium can be created on the surface of nanotube bundles. Specifically, when $^4He$ is first adsorbed on nanotubes, it forms a 1D linear solid along the grooves between two nanotubes on the bundle surface with lattice parameter, a$_1$ = 3.40 $\pm$ 0.02 \AA. When more helium is added, 2D solid helium covers the whole bundle surface. We have now determined the vibrational dynamics of these 1D and 2D solids, the dynamic structure factor, $S(Q,\omega)$. From the inelastic intensity integrated over all $\omega$ we obtain the MS amplitude of vibration along 1D chain $\langle u^2\rangle = 0.28$ \AA$^2$or Lindemann ratio $\gamma = (\langle u^2\rangle)^{1/2}/a_1 = 0.15 $ which is less than the bulk solid value near melting. The vibrational density states (DOS) of the 2D solid shows a gap at $\omega\simeq$ 0.75 meV indicating a commensurate solid as found for $^3He$ and $^4He$ on graphite surfaces. In contrast the 1D DOS shows little or no gap and the DOS goes uniformly to zero as $\omega \rightarrow 0$. [1] Pearce et al. Phys. Rev. Lett. 95, 185302 (2005).   

100-fold reduction of 2D spin-polarized hydrogen gas's clock-shifts explained

Recent experiments have observed that when two-dimensional spin-polarized hydrogen is absorbed on a superfluid helium film, the density dependent shift of the 1S-2S spectral line (clock shift) is 100 times smaller than expected [1]. By studying the theory of interactions between hydrogen atoms and the helium surface, we show that helium-mediated hydrogen-hydrogen interactions dramatically reduce the clock shift. The mediated potential is sensitive to experimental parameters, such as temperature and $^3$He concentration. This explains another mysterious experimental result: we find that increasing $^3$He concentration increases the clock-shift, as observed. In contrast, the naive picture which neglects mediated interactions predicts the clock-shift to decrease with $^3$He concentration due to deconfinement of the hydrogen gas. [1] J. Ahokas, J. J\"arvinen, and S. Vasiliev, Phys. Rev. Lett. \textbf{98}, 43004 (2007).   

Bound spin waves in the ferromagnetic layer of $^3$He on highly oriented graphite

The second monolayer of $^3$He on graphites such as Grafoil becomes highly ordered at millidegree temperatures. This system is a good model for nanoscale two-dimensional magnetism because of the large number of separated two-dimensional planes. Motivated by our interest in increasing the structural coherence of the graphite samples that we study, we have used exfoliated ZYX grade graphite as a substrate for our recent experiments. Much of the general picture of finite temperature ordering with ZYX is similar to Grafoil. However, as a byproduct of our increased structural coherence, we have observed several distinct resonances in the ordered spin system. This result is surprising because the structural size of platelets of graphite is not controlled. Nevertheless, the separation of the resonances is consistent with bound two-dimensional spin waves with length scales consistent with the average sizes of the graphite platelets. We will present our analysis of the temperature dependence of the spin wave modes.   

Spin Pumping in Superfluid $^3$He in High Magnetic Field

The spin flow dynamics in superfluid $^3$He A$_1$ phase in magnetic field has been studied up to 13 tesla. The apparatus consists of a large reservoir of of A$_1$ phase in which a small enclosed chamber with a built-in differential pressure sensor is immersed. The chamber is connected to the reservoir via a superleak channel. The chamber is fabricated from Macor parts such that the residual heat leak is much reduced from those in our experiments. Our focus is on the measurement of relaxation of the induced pressure subsequent to either magnetically induced spin-polarized superflow or by electrostatic spin pumping. In general, both methods of measurement show that the relaxation time ($\tau$) of the induced pressure tends to vanish smoothly as the transition temperature T$_{c2}$ is approached. However, the observed dependence of $\tau$ on magnetic field is different. The measured $\tau$ by the field gradient method continues to increase up to 8 tesla. On the other hand, $\tau$ measured by the spin pumping method tends to saturate to a constant between 5 and 13 tesla. The discrepancy is unexpected and not yet understood.   

Discovery of a New Excited Pair State in Superfluid $^{3}$He

In superfluid $^{3}$He, the order parameter collective modes correspond to excited states of the $^{3}$He Cooper pairs and are classified by their total angular momentum, \textit{J = L + S}. Many of these modes with $J \le $ 2 have been experimentally observed through longitudinal sound measurements or NMR. As a result of coupling to the collective mode with $J $= 2 and $m_{J }=\pm $1 there is an enhanced restoring force for transverse sound in superfluid $^{3}$He-B. Previously, we have used the interference of transverse sound waves to study this collective mode. Recently we have discovered a new coupling to transverse sound near the pair-breaking threshold with the classic signatures of a collective mode. Application of a magnetic field results in circular acoustic birefringence and a new acoustic Faraday effect, from which we extract the corresponding Verdet constant. Selection rules for the coupling to transverse sound and acoustic birefringence require this mode to have $J \ge $ 4, suggesting that this mode is most likely the $J $= 4 ($m_{J }=\pm $1) mode resulting from an attractive $f$-wave pairing interaction in this $p$-wave superfluid.   

Direct Sound Propagation in Superfluid $^{3}$He-A in 98\% Aerogel

Liquid $^{3}$He impregnated in high porosity aerogel has been studied extensively in recent years since its unique structure provides static impurities in this system. The fragile nature of p-wave Cooper pairs against impurity was clearly demonstrated by the significant depression of the superfluid transition. The scattering off the aerogel also significantly modifies the low energy excitation by inducing impurity bound states inside the gap. Recent ultrasound attenuation measurements performed in the B-like phase of superfluid $^{3}$He in 98\% porosity aerogel revealed many interesting features and provided strong experimental evidence of gapless superfluidity. We conducted high frequency sound propagation measurements at 6.22 MHz in the A-like phase of superfluid $^{3}$He. The A-like phase is stabilized by magnetic fields (up to 4 kG) applied perpendicular to the direction of sound propagation. We present our preliminary results of ultrasound attenuation down to the zero temperature limit at 29 bar and the field dependent A-B transition identified by the jump in attenuation.   

Effect of Global Anisotropy on Superfluid $^{3}$He in Compressed Aerogels

The importance of anisotropic scattering on the superfluid phases of $^{3}$He has been addressed recently and experiments using uniaxially distorted aerogel have been proposed in order to elucidate the influence of global anisotropy on the A-B transition $\footnote{C. L. Vicente {\it et al.}, Phys. Rev. B 72 094519 (2005).}$$^{,}$$\footnote{Kazushi Aoyama and Ryusuke Ikeda, Phys. Rev. B 73, 060504(R) (2006).}$. We performed high frequency transverse acoustic impedance measurements on superfluid $^{3}$He confined in 98{\%} porosity aerogel at 29 bar. The aerogel cylinder is compressed along the symmetry axis to generate global anisotropy. With 10{\%} axial compression, our measurements reveal that the A-like to B-like transition is absent on cooling down to $\approx $300 $\mu $K in the absence of magnetic field and in magnetic fields up to 3 kG. This behavior is in contrast to that in uncompressed aerogels, in which the supercooled A-like to B-like transitions have been identified by various experimental techniques. Our results are consistent with the theoretical prediction by Aoyama and Ikeda.   

Low field NMR in aerogel-confined superfluid $^3$He

The superfluid states of bulk liquid $^3$He were convincingly identified through their longitudinal and transverse NMR spectra. The order parameters of the superfluid phases of $^3$He confined within aerogel have generally been assumed to be identical to those in bulk liquid. While that identification has not been contradicted by experimental data, it has not yet been tested as carefully as in bulk. Fomin has suggested that the A-like phase in aerogel could be an axiplanar state, distinct from the bulk axial state. We have tested the identification by studying low-field NMR which is more sensitive to the distinction between the candidate states. Using the dc SQUID based NMR detection system developed in our laboratory over many years we have studied both longitudinal and transverse resonance spectra in 99.5\% porosity aerogel in magnetic fields of 1-4 mT, an order of magnitude lower than previous NMR work. Our work shows qualitative features similar to those found in higher magnetic fields. While we were unable to resolve the longitudinal resonance, transverse resonance measurements exhibit a characteristic field- and temperature-dependence.   

Dynamics of Quantum Vortices

Quantized vortices exist in systems ranging from low-T magnets, to superfluids and superconductors; however, their dynamics remain controversial. Even the existence of a force acting transverse to the motion (like a Lorentz force) relative to thermal quasiparticles has been widely debated. Quite remarkably, it remains unresolved just what forces act on a quantum vortex. From an influence functional calculation, we show that the expected log divergent mass generalizes to a frequency dependent mass and damping, which, in time, manifest as memory dependent damping forces, acting both longitudinal and transverse to current motion. Because topological properties are involved, our results apply equally to quantum vortices in many different systems. For instance for vortices in insulating magnets, we are able to find the various forces, including those resulting from vortex-magnon interactions, and derive their dynamics. In contrast to superfluids and superconductors, an experimental test in insulating magnets should be possible using existing methods.