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Low Temperature Physics

On paired nature of superfluid condensate in helium-II

S. I. Vilchinskiĭ, Ernst A. Pashitskii, P. I. Fomin

Published Dec 1, 1997• 5 citations
Publisher

Abstract

A hypothesis on pairing of helium atoms below the λ-point is put forth on the basis of empirical data on the dynamics of He3 impurity atoms in superfluid He4, that suggest an abnormally large effective mass of He3. The role of paired condensate in superfluidity of He4 is considered as well as the possibility of additional experimental proofs of the pairing of He4 atoms, including the observation of vortices with a half-integral velocity circulation quantum.

DOI
10.1063/1.593502

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Physical Review B•Jul 26, 2006•6 citations
A hypothesis on pairing of helium atoms below the λ-point is put forth on the basis of empirical data on the dynamics of He3 impurity atoms in superfluid He4, that suggest an abnormally large effective mass of He3. The role of paired condensate in superfluidity of He4 is considered as well as the possibility of additional experimental proofs of the pairing of He4 atoms, including the observation of vortices with a half-integral velocity circulation quantum.
The paradoxes and disparities in the contemporary microscopic theory of superfluid helium (He–II) are discussed along with possible ways of resolving them by taking pair correlations of He4 atoms into consideration. It is shown that most paradoxes are associated with the commonly accepted initial assumption concerning the dominating role of single-particle Bose condensate (SPBC) in the quantum microstructure of the superfluid component ρs. The existence of intensive SPBC leads to a strong hybridization of the elementary excitation branches and to a common dispersion law for all boson branches, which is identified with the quasiparticle spectrum E(p) observed experimentally from slow neutron scattering in liquid helium. However, the stability of this spectrum during a transition through the λ-point and the large value of the gap in the vicinity of the “rotonic” minimum contradict both the Landau theoretical criterion of superfluidity and the small value of experimentally measured critical velocity. At the same time, a strong interaction between particles in the Bose liquid He4 strongly suppresses the SPBC which amounts to less than 1% of all He4 atoms and hence cannot be the main constituent of the superfluid component, unlike the case of a weakly nonideal Bose gas. Moreover, for a quite strong attraction between particles in a certain region of the momentum space, bound pairs of bosons can be formed in the superfluid Bose liquid, and a coherent pair condensate (CPC) analogous to the Cooper pair condensate in superconductors may appear. Such a strong CPC may completely suppress the weak SPBC. In this case, the one-particle spectrum ε(p) of elementary excitations does not hybridize with the collective (two-particle) spectrum and does not appear in the structure of the dynamic form factor S(p,ε), i.e., does not coincide with the spectrum measured from neutron scattering. The dispersion of one-particle spectrum is defined by the momentum dependence of the pair order parameter Ψ̃(p) and may have a minimum or a point of inflection at p≠0. This peculiarity in the one-particle spectrum of a Bose liquid with CPC but without SPBC vanishes together with Ψ̃(p) at the temperature Tc=Tλ of the phase transition from the superfluid to the normal state (unlike the rotonic minimum in the collective spectrum), while the corresponding critical velocity vc=min[ε(p)/p] vanishes at the λ-point in accordance with the Landau criterion and the experimental data. The assumption that the strong “Cooper-like” CPC is responsible for the quantum structure of the superfluid component ρs is confirmed indirectly by the successful application of the Justrow approximation (based on strong pair correlations) for describing the properties of liquid He4 and quantum liquid mixtures He3–4He on one hand, and by an anomalously large effective mass of He3 impurity atoms in He4, which is approximately equal to total mass of He3 and He4 atoms, thus pointing to the existence of helium atoms in superfluid liquid He–II. The value of the superfluid velocity circulation quantum in the Onsager–Feynman vortices in a Bose liquid with CPC but without SPBC is discussed as well as the critical velocities of superfluid He4 in ultrathin films and channels in which the creation and motion of quantum vortices are ruled out, and the quasiparticle spectrum undergoes dimensional quantization.
Since 1974 there have been serious experimental and also theoretical pointers to the possibility that no Bose condensation occurs in superfluid He4. Evans presented a theoretical argument against a condesate, suggesting a “pairing” model of superfluid helium. As yet, experiment connot decide if the concept of a one-particle condensate can be replaced by the idea of a two-particle condensate. March and Galasiewicz have argued that, if there is no one-particle condensate in He4, a ground state wave function cannot be built from a product of pairs but must fundamentally include three-particle correlations at least. So the idea of a three (not two) particle condensate seems worth some attention. It is demonstrated here that assuming a three-particle condensate we can regain from microscopic theory the Landau hydrodynamic equation for the superfluid velocity.
The magnitude, sign, and momentum dependence of the effective interaction between He3{\mathrm{He}}^{3}He3 atoms in superfluid He4{\mathrm{He}}^{4}He4 are derived from the experimental data. Calculations of the Fermi-liquid parameters for the normal state of He3{\mathrm{He}}^{3}He3 in solution yield results in agreement with experiment; the temperature for a superfluid transition associated with the He3{\mathrm{He}}^{3}He3 is estimated to be \ensuremath{\sim}2\ifmmode\times\else\texttimes\fi{}${10}^{\ensuremath{-}6}$ \ifmmode^\circ\else\textdegree\fi{}K.
This book is about a certain class of superfluids, namely the high temperature superconductors. Perhaps the simplest of the superfluids is liquid He4. Since the very early days of quantum mechanics it has been known that the helium atom He4 is a boson; it is built of an even number of particles (two electrons, two neutrons and two protons), so that a wave function ^(ri,F2) must be symmetrical in FI — r? where FI, r-z are the electron's coordinates. This has the result that half the rotational states of the molecule H62 are absent and that the scattering of alpha particles by helium for low energies deviates from the Rutherford scattering law. It also has the remarkable result that this is not so for the light isotope He3, which shows that the number of neutrons in the nucleus affects properties depending otherwise only on the electrons and nuclear charge.
This chapter describes a system of interacting bosons at very low temperatures. For helium, the forces are relatively weak, while, because of its low mass, the zero-point oscillations of the individual atoms are large. The low temperature phase is called He II; the high temperature phase, He I. Indications of the existence of He II were already present in the early experiments of Kamerlingh Onnes. The "superfluidity" of He II was discovered independently, and essentially, simultaneously, by Kapitza and Allen and Misener, by studying the flow of liquid helium through a thin capillary. In the two-fluid model, superfluid He II is regarded as being composed of two fluids which are simultaneously present and mutually interpenetrating. The superfluid component is the condensate, the single condensed quantum state of the Bose liquid. The existence of superfluid flow through a narrow capillary is built into the theory.
The basic assumption of this paper is that in the presence of Bose-Einstein condensation (BEC) in liquid 4He^{4}\mathrm{He}4He, the wave functions of occupied many particle states are the superposition of two components; a phase coherent component, proportional to the ground state wave function and a phase incoherent component. It is shown that this assumption satisfies necessary conditions imposed by the presence of BEC and that the wave functions of the ideal Bose gas and wave functions of the Bijl-Feynman type are of this form. It is shown that this single assumption provides simple microscopic explanations of essentially all the exotic properties of helium II; why BEC implies two fluid behavior, how the superfluid and condensate fractions are linked, how Landau theory is linked to the presence of BEC, why the superfluid exhibits flow without viscosity and macroscopic quantum effects while the normal fluid does not, how the anomalous expansion and loss of spatial order, observed in helium II as it is cooled, is linked to BEC, and how the presence of sharp peaks observed in the dynamic structure factor are linked with BEC. The theory provides predictions that are in quantitative agreement with a wide range of presently unexplained experimental data on helium II.