Liquid helium in confinement

Transcription

1 J Phys. IVFrance 10 (2000) O EDP Sciences, Les Ulis Liquid helium in confinement B. Fgk, 0. Plantevin and H.R. Glyde* Depattement de Recherche Fondamentale sur la Matiere Condensee, SPSMS/MDN, CEA Grenoble, Grenoble cedex 9, France * Depattment of Physics and Astronomy, University of Delaware, Newark, Delaware , U. S. A. Abstract. We discuss the effects of confinement and disorder on the elementary excitations of superfluid 4 ~ in e porous media as observed by inelastic neutron scattering. The three-dimensional bulk-like phonon-roton excitations of liquid 4 ~ in e aerogel and Vycor are the same as in bulk 4 ~ at e low temperatures, with the same temperature dependence. In addition to these excitations, two-dimensional layer modes, which propagate in the first few liquid layers close to the substrate, are observed in both Vycor and denser aerogels near the roton wave vector, with a rotonlike dispersion. 1. INTRODUCTION Liquid 4He in porous media is a key example of a strongly interacting Bose system in confinement and disorder. When superfluid 4He is confined in porous media such as aerogel or Vycor, the macroscopic properties, and in particular the superfluid density and the superfluid transition temperature, are modified [I]. Theoretical model calculations and simulations of the excitations in superfluid 4 ~ in e disorder predict a softening of the phonon energy and additional excitations at low energies [2]. For the past five years, a number of inelastic neutron scattering experiments has been performed to study the microscopic dynamics of superfluid 4He in porous media [3-1 I]. These measurements, which probe the density fluctuations through the dynamic structure factor S(Q,o), have been made on a variety of instruments, such as triple-axis, direct and inverted time-of-flight, and back-scattering spectrometers, using different energy resolution. The broad picture emerging from these studies is that liquid 4He in porous media supports elementary phonon-roton excitations having the same energies and lifetimes at all temperatures as in bulk 4He. However, there is additional intensity in the tail of the roton peak, which can be attributed to two-dimensional (2D) layer modes propagating in the liquid layers adjacent to the substrate. These layer modes resemble those observed in films of superfluid 4He on graphite surfaces [12]. They are also important in explaining the specific heat and the superfluid density at low temperature in Vycor, for example. The most popular porous media that have been studied are aerogel and Vycor. Aerogel has a highly tenuous structure of irregularly connected silica (SiO2) strands with a large distribution of pore sizes, from a few to a few hundred A. The aerogels used for neutron scattering measurements have porosities in the range from 87 to 96%. To reduce the incoherent elastic scattering from hydrogen impurities in form of OHgroups attached to the walls of the aerogel, some samples have been deuterated, either by exposing the gel to deuterium gas, or more efficiently, by growing it from deuterated chemicals. The superfluid transition temperature in aerogels is reduced by only a few mk compared to the bulk. Porous Vycor glass is fabricated by leaching out the B203-rich phase of a phase-separated borosilicate glass. The result is a sponge-like silica-rich material, where the open pores constitute approximately 30% of the total volume. The pores comprise an open network of highly interconnected channels of a typical diameter of 70 A. Vycor contains approximately 3.5% B2O3, which due to the large neutron absorption cross-section of the l0b isotope strongly reduces the scattered intensity. However, this problem can be avoided if the natural boron Article published online by EDP Sciences and available at

2 Pr7-164 JOURNAL DE PHYSIQUE IV is replaced by the 11B isotope, which has negligible absorption. In Section 2 and 3, we will discuss the main results of inelastic neutron scattering measurements on helium in Vycor and aerogel, respectively. Section 4 concludes the paper. 2. VYCOR We have measured the dynamic structure factor S(Q,o) of superfluid 4He in a specifically prepared Vycor sample made from 99.95% llb-enriched B203 in order to reduce the neutron absorption. Well-defined phonon-roton excitations are observed at low temperatures for all wave vectors in the range 0.4<Q<2.1 A-1, and the dispersion of this 3D bulk-like mode, shown in Fig. la, is identical to that of bulk 4He, measured in the same experiment [9]. The energy and width of the phonon-roton excitations of helium in Vycor, and their temperature dependencies, are the same as in bulk 4He, within the experimental precision (typically 5-10 pv). o Vycor (3D) Bulk ----e.-- Vycor 2D 1 Q (A-') Energy (mev) Figure 1. Excitations of superfluid 4 ~ in e Vycor measured on the time-of-flight spectrometer IN6 with an energy resolution of 110 pev at T=0.5 K. (a) Dispersion curve. The open circles show the three-dimensional bulk-like phonon-roton dispersion of helium in Vycor, which is identical to that of bulk 4 ~ (solid e line) measured in the same experiment. The dispersion of the two-dimensional layer modes is shown by closed circles and dotted line. (b) Dynamical structure factor at the roton wave vector for helium in Vycor (closed circles and solid line) and in bulk 4 ~ (open e circles and dotted line). Additional intensity due to layer modes is clearly seen in the low-energy tail. The main peak is shown as a solid line after reduction by a factor of 20. An example of a spectra at the roton wave vector is shown in Fig. lb. In addition to the main peak, which corresponds to the 3D bulk-like roton, there is additional intensity in the low-energy tail of the peak, which is absent in the measurements on the bulk liquid. This additional intensity, which was first observed by Dimeo and co-workers [8], can most likely be attributed to 2D layer modes, similar to those existing in helium films on graphite. Due to the improved statistics in the present experiment, resulting from the use of isotopic Vycor, we have determined the dispersion of the 2D layer mode with precision. It can be described by the same expression used for the bulk roton, o = A + (Q-Q~)~/(~P), with the same roton wave vector QR and curvature p, but where the energy gap A is 0.55 mev compared to 0.74 mev in the bulk. The energy gap of the layer mode is the same as the gap extracted from specific heat and superfluid density measurements at low temperatures. The temperature dependence of S(Q,o) for helium in Vycor at a wave vector somewhat below the roton is shown in Fig. 2 as solid symbols (the bulk liquid measured in the same set-up is shown by the lines). At the lowest temperature, there is a well defined phonon-roton excitation in S(Q,o). With increasing temperature, the peak broadens, shifts down to slightly lower energies, and the integrated

3 DYNAMICS IN CONFiINEMENT Pr7-165 intensity in the peak decreases. At the highest temperatures, T=2.31 K, there is no discernible peak in S(Q,o). However, at T = 1.99 K, which is above the superfluid transition temperature in Vycor (Ts = 1.95 K [I]) but below the bulk value for Th=2.17 K, there is still a thermally broadened peak. This intriguing finding may have important consequences, as we will now discuss. In bulk 4He, it has been observed that for wave vectors above the maxon wave vector Q>l. 1 A-1, the weight of the well-defined peak in S(Q,o) scales with temperature approximately as the superfluid density ps(t) Above the superfluid transition, where ps = 0, there was no well-defined peak in S(Q,o). Glyde and Griffin (GG) [14] have suggested that this scaling arises because the elementary excitations involve the excitation of quasiparticles out of the condensate and that the scaling variable is the Bose-Einstein condensate fraction no(t) rather than ps(t). Here, we observe that the weight of the sharp excitation peak in S(Q,o) does not scale with ps(t) in Vycor. The deviation is large and there remains a peak in S(Q,o) above Ts where ps = 0. Thus the apparent scaling of peak weight with ps(t) in bulk 4He is not universal and does not extend to confined geometries. However, the excitation weight in S(Q,o) in Vycor might still scale with no(t) (as in bulk 4He) if no(t) in Vycor were similar to bulk 4He, and particularly if no(t) were finite between Ts = 1.95 K and Th = 2.17 K. Thus, either the GG proposal is incorrect or there remains a condensate in 4He in Vycor above Ts, perhaps up to Th. If there is a condensate above T,, then we are observing the separation of the superfluid transition temperature Ts from the Bose- Einstein condensation temperature by disorder or confinement. This puzzling possibility requires further measurements of S(Q,o) and of no directly O 1.2 Energy (mev) Figure 2. Dynamic structure factor S(Q,o) of liquid 4 ~ in e Vycor (closed symbols) at Q = 1.7 A-1 at different temperatures, measured on IN6 with an energy resolution of 110 pv. The statistical errors are smaller than the symbol size. The lines show bulk data for comparison. 3. AEROGEL The dynamic structure factor of helium in aerogel is very similar to that in bulk helium at all temperatures. In some earlier studies on aerogels with porosities of the order of 95% [4,6], a small broadening of the order of a few pev of the roton excitation was reported at low temperatures. However, the observed effect was considerably smaller than the resolution width, and thus subject to artefacts if the shape of S(Q,o) of helium in aerogel is slightly different from that in bulk helium. In fact, subsequent high-resolution

4 Pr7-166 JOURNAL DE PHYSIQUE IV measurements by Anderson et al. [7] showed no broadening of the roton peak at low temperatures, at the level of a fraction of a pev. We have recently measured S(Q,o) in a denser aerogel with 87% porosity, and these measurements show the existence of additional intensity in the low-energy tail of the roton peak (Fig. 3a). By studying the filling dependence of S(Q,o) for fillings between 30 and loo%, we find that the additional intensity can be related to 2D layer modes that propagate in the first few liquid layers above the substrate, as discussed in detail in Ref. [lo]. This is the first time such layer modes have been observed in fully filled aerogel. This additional intensity, which was not resolved in earlier studies of less dense aerogel, makes the elementary excitation peak appear broader if the intensity is not resolved and subtracted. We have also made detailed measurements of the temperature dependence of the energy of the bulk-like roton in fully filled aerogel using different aerogels and different spectrometers with different energy resolution. The results shown in Fig. 3b include data for aerogel with porosities ranging from 87 to 95% measured on different spectrometers with energy resolutions between 50 and 100 pev, as detailed in the figure caption. The temperature dependence of the roton energy in these aerogels is in excellent agreement with that of the bulk roton (see Fig. 3b), measured in the same set-up under identical conditions. Hence, there is no difference between the roton energy in helium in aerogel and bulk helium at any temperature in our measurements. This result is in disagreement with some other work [5], and the reason for this discrepancy is not fully understood. A higher roton energy could possibly be observed at intermediate temperatures if the multiple scattering, which is centered mainly above the roton peak, is not carefully corrected for. In our measurements, this problem is avoided by using fully deuterated aerogels, for which the multiple scattering is negligible. As mentioned, theoretical work have suggested a softening of the phonon velocity of helium in porous media. Neutron scattering measurements at a wave vector of Q=0.2 A-1 [6], the lowest achievable due to the strong elastic scattering at small wave vectors from the large-scale structure of aerogel, do not show any modification of the phonon energy, at a level of 2% of the phonon energy (or velocity). 4. CONCLUSION d - - I I I I - 4 ~ in e aerogel Q=1.93A-' Instrument 1 resolution IN12 50peV A IN6 100p,eV 660- IN12 100peV -- Bulk helium lsls expts Energy (rnev) Neutron inelastic scattering studies of superfluid 4He in porous media such as aerogel and Vycor show that the three-dimensional bulk-like phonon-roton excitations are the same as in bulk 4He, with the same temperature dependence. The main difference compared to bulk helium is the existence of additional two- I I-OT (lg Figure 3. (a) Dynamic structure factor S(Q,w) of liquid 4 ~ in e 87% porous aerogel at Q=2.1 A-1 and T=0.5 K (closed symbols and solid line), measured on IN6 with an energy resolution of 110 pev. The dashed line shows the additional intensity identified as due to layer modes. Bulk data are shown for comparison (crosses and dotted line). (b) Temperature dependence of the bulk-like roton energy in different aerogel samples measured at the ILL (closed symbols) and at ISIS (open symbols) compared to bulk 4 ~ (line). e Closed circles: aerogel with 87% porosity measured on IN12 with an energy resolution of 46 pev; triangles: aerogel with 87% porosity measured on IN6 with an energy resolution of 110 pev, squares: aerogel with 95% porosity measured on IN12 with an energy resolution of 110 pev [6]; open circles: aerogel with 90 and 95% porosity measured on IRIS [5].

5 DYNAMICS IN CONFINEMENT Pr7-167 dimensional layer modes, observed in both Vycor and denser aerogels near the roton wave vector. These modes have a roton-like dispersion, with an energy gap that is smaller than in bulk helium, and which depends on the material. Acknowledgments We are grateful to J.R. Beamish and N. Mulders for providing the fully deuterated aerogel samples, to J. Bossy, G. Coddens, and H. Schober for assistance with the experiments, and the Institut Laue- Langevin for providing the cryogenic equipment. This work was partially supported by the National Science Foundation, grant DMR References [I] M.H.W. Chan et al., Phys. Rev. Lett. 61, 1959 (1988). [2] L. Zhang, Phys. Rev. B 47, (1993); W. Krauth and N. Trivedi, Europhys. Lett. 14, 627 (1991); W. Krauth, N. Trivedi, and D.M. Ceperley, Phys. Rev. Lett. 67, 2307 (1991); M. Makivic, N. Trivedi, and S. Ullah, Phys. Rev. Lett. 71, 2307 (1993); M. Boninsegni and H.R. Glyde, J. Low Temp. Phys. 112, 251 (1998). [3] J. de Kinder, G. Coddens, and R. Millet, Z. Phys. B 95, 51 1 (1994); G. Coddens, J. de Kinder, and R. Millet, J. Non-Cryst. Solids 188, 41 (1995). [4] M.R. Gibbs et al., Physica B , 462 (1995). [5] P.E. Sokol et al., Nature 379, 616 (1996); M.R. Gibbs et al., J. Low Temp. Phys. 107, 33 (1997); R.M. Dimeo et al, Phys. Rev. Lett. 79, 5274 (1997). [6] 0. Plantevin et al., Phys. Rev. B 57, (1998). [7] C.R. Anderson et al., Phys. Rev. B 59, (1999). [8] R.M. Dimeo et al., Phys. Rev. Lett. 81, 5860 (1998). [9] H.R. Glyde et al., Phys. Rev. Lett., in press. [lo] B. F& et al., submitted to Phys. Rev. Lett. [l Plantevin et al., these proceedings. [12] W. Thomlinson, J.A. Tarvin, and L. Passell, Phys. Rev. Lett. 44, 266 (1980); H.J. Lauter et al., Phys. Rev. Lett. 68, 2484 (1992); H.J. Lauter et al., J. Low Temp. Phys. 87, 425 (1992); B.E. Clements et al., Phys. Rev. B 53, (1996). [13] A.D.B. Woods and E.C. Svensson, Phys. Rev. Lett. 41, 974 (1978) H.R. Glyde and A. Griffin, Phys. Rev. Lett. 65, 1454 (1990).