An evaluation of the average superfluid density of 4He in a cylindrical pore near T
λ predicted by the Ginzburg-Pitaevskii-Mamaladze theory

Bot, L. V.; Schubert, P. C.; Zimmermann, W.

doi:10.1007/bf00115077

J Low Temp Phys

1981

DOI: 10.1007/bf00115077

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An evaluation of the average superfluid density of 4He in a cylindrical pore near T λ predicted by the Ginzburg-Pitaevskii-Mamaladze theory

L. V. Bot

P. C. Schubert

W. Zimmermann

Abstract: A numerical evaluation of the average superfluid density of 4He in a cylindrical pore near T a predicted by the Ginzburg-Pitaevskii-Mamaladze theory has been carried out as a function of pore radius and temperature. The results are presented in graphical form and in terms of an accurately fitting closed algebraic form.The only detailed prediction for the behavior of the superfluid density ps of 4He in a cylindrical pore of which we know is provided by the free-energyexpansion theory of Ginzburg and Pitaevskii … Show more

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Cited by 10 publications

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“…The numerical coefficient k is found to depend slightly on the ratio £(T)/R and to vary between 2.2 and 2.7. The same problem has been treated for superfluid 4 He confined in cylindrical tube by Bot, Schubert, and Zimmermann, 9 who showed that the same depression of superfluid density is expected as given by Eq. (l) with /c=2.4.…”

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confidence: 72%

Healing Length of SuperfluidHe3

Ichikawa¹,

Yamasaki²,

Akimoto³

et al. 1987

Phys. Rev. Lett.

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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...

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confidence: 72%

Healing Length of SuperfluidHe3

Ichikawa¹,

Yamasaki²,

Akimoto³

et al. 1987

Phys. Rev. Lett.

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Measurements of superfluid densities and critical superfluid mass currents of pure 4He and 3He/4He mixtures in nuclepore near the lambda transition

Schubert

Zimmermann

1981

J Low Temp Phys

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Measurements have been made of the relative superfluid density psp/ p and the critical mass currentIsc for the onset of dissipation in the superfluid flow of pure 4He and 3He/4He mixtures in the circular cylindrical pores of Nuclepore near the h transition, using a double-ended Helmholtz resonator. Pore diameters of O. 03, O. 1, and 0.4 tzm were studied using 3He mole fractions of O. O, ~ 0.2, and 0.4. For each pore diameter dp and mole fraction x our results for psp/ p were • 0 675 fitted relattvely well by the form C(t-to1) " and those for Isc by the form I~co(t-to~) g, where t=-[Tx -T]/Tx. For each combination of dp and x the reduced onset temperatures to1 and toc are in rough agreement with each other but somewhat larger than values found by others for Nuclepore. For the smaller two pore diameters, these onset temperatures are consistent with the unithat near Tx, h p~b~/m4kBT should be a constant versality hypothesis 2 e independent of T and x. Here h is the reduced Planck constant, P~b is the bulk superfluid density, ~ is the coherence length, m4 is the 4He atom mass, kB is Boltzmann ' s constant, and T is the absolute temperature. At each value of x the amplitudes C agree well with the corresponding amplitude for Psb/P, and g equals 1.17 + 0.04 for all cases. Measurements of the velocity of second sound at x = 0. 000, 0.190, 0.401, and 0.450 are also reported.

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The effect of a magnetic field on fourth sound in 3He

Daly

1988

J Low Temp Phys

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The influence of a magnetic field on the propagation o f fourth sound in superfluid 3He is studied. The field and temperature dependences of the average superfluid density Ps/ P and fourth sound Q are measured. The field dependence Of ~s/ p is very different in a porous medium than predicted by Ginzburg-Landau theory applied to bulk liquid. In particular, a magnetic suppression of ~s/ p is observed in the temperature and pressure ranges corresponding to the A phase in bulk liquid. There is strong evidence of a magnetic suppression of T c itself. The measured ps/ P has a slight history dependence in a magnetic feld, but none in zero field. The fourth-sound Q values are compared to the theoretical work of Smith, Jensen, and Wolfle. Quantitative confirmation of their work is problematic.

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An evaluation of the average superfluid density of 4He in a cylindrical pore near T λ predicted by the Ginzburg-Pitaevskii-Mamaladze theory

Cited by 10 publications

References 2 publications

Healing Length of SuperfluidHe3

Healing Length of SuperfluidHe3

Measurements of superfluid densities and critical superfluid mass currents of pure 4He and 3He/4He mixtures in nuclepore near the lambda transition

The effect of a magnetic field on fourth sound in 3He

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