Healing Length of SuperfluidHe3

Abstract

Using fourth-sound techniques, we have measured the depression of the superfluid fraction of 3 He confined in small pores of packed powder over wide temperature (0.2 < T/T c <1) and pressure (0.5 < p < 20 bars) ranges. From the analysis of the data we determine the magnitude and the pressure dependence of the healing length. The healing length decreases from 520 A at 0.5 bar to 200 A at 20 bars. The values are in fair agreement with those expected from the BCS expression.PACS numbers: 67.50.Fi, 74.50.-l-r When a superfluid is confined in a sufficiently restricted geometry, the macroscopic order parameter describing the superfluid state becomes distorted by the presence of the boundary wall. 1 " 3 The nature of distortion will be determined by the particular boundary conditions that the wall imposes on the order-parameter function. Theoretical and experimental studies aimed at probing the boundary conditions for superfluid 3 He are currently under active research. 4 Understanding that the boundary conditions will be important in the design of an appropriate weak link for observing the long-sought analog of the Josephson effect in superfluid 3 He. 5 ' 6 Interpretation of experiments on superfluid-3 He films will be related to the boundary conditions. An important parameter in these phenomena is the healing length which determines the characteristic distance over which the order parameter decreases from its bulk value to zero near a wall. In this paper we describe a systematic determination of the healing length over a wide pressure range from the analysis of the measured superfluid fraction of 3 He confined in the pores of packed powder.Ambegaokar, de Gennes, and Rainer 1 showed that the nature of scattering of quasiparticles at a solid wall plays a crucial role in the determination of the boundary conditions. If the scattering is completely diffusive, they showed that the perpendicular (to the wall surface) component of the order parameter vanishes at the wall and that the parallel component is depressed from the bulk value by a factor of ~£O/£(JT). Here £n is the zerotemperature coherence length and %(T) is the temperature-dependent healing length. Recently, Buchholtz 7 showed that if the surface is bumpy at random on the scale of inverse Fermi wave number (~5 A) the parallel component also vanishes at the surface. It seems reasonable to assume that the powder used in our experiment presents diffuse scattering surfaces and that all components of the order parameter vanish at the surface.The Ginsburg-Landau (GL) equations, including the gradient terms for superfluid 3 He, have been derived by Ambegaokar, de Gennes, and Rainer. ] The GL equations define a natural length scale given by the healing length for the spatial variation of the order parameter. Minimizing the GL free-energy functional by variational calculation, Ebisawa and Arai 8 have shown that if a cylindrical pore of radius R is filled with superfluid 3 He-Z? whose order parameter obeys the above boundary conditions, the average superfluid density in th...

Quantum Phase Transition of3Hein Aerogel at a Nonzero Pressure

“…This self-purification of 3 He has made it impossible to introduce disorder or impurities into the system. Experiments show that 3 He superfluids in aerogel display behavior [1][2][3] very different from earlier studies in confined geometries where diffuse surface scattering that suppresses T c dominates [4] and the size distribution smears out the sharp magnetic and mechanical responses of the bulk [5,6,7]. It was generally believed that p-wave superfluids are easily damaged by disorder [8], but the newest experiments [1][2][3] show that notwithstanding the T c suppression, superfluid coherence remains robust in aerogel.…”

Heat Capacity ofH3ein Aerogel

“…The 1995 discovery of the superfluid transition of 3 He in aerogel glass [1] [2], has aroused wide interest. The 3 He-aerogel system presents a unique opportunity for study of the influence of quenched impurities on the wellunderstood system of pure superfluid 3 He.…”

“…We are thus able to correlate features in the heat capacity with the dynamic superfluid response. The liquid 3 He within the apparatus is cooled by a silver sinter pad, which is thermally clamped to a PrNi 5 nuclear cooling stage. There are two lanthanum diluted cerium magnesium nitrate (LCMN) thermometers; one inside the sample cell and the other located near the silver sinter.…”

“…We also note that in addition to the linear term in this region there appears to be a small additional constant contribution to the heat capacity (≈ 10µJ/K). Golov and Pobell suggest that this contribution may arise from ordering in the amorphous solid 3 He layer [19]. Since our main interest is in the heat capacity associated with the 3 He-aerogel superfluid transition, we shall subtract the bulk 3 He heat capacity contribution.…”

“…The 3 He-aerogel system presents a unique opportunity for study of the influence of quenched impurities on the wellunderstood system of pure superfluid 3 He. Earlier studies employing other porous media such as sintered silver or packed powders [3] [4] were dominated by surface scattering and finite size effects [5]. Aerogel consists of a fractal structure of relatively uniform silica strands 30Å in diameter.…”