J. Phys. France
Volume 49, Number 8, août 1988
Page(s) 1411 - 1423
References of J. Phys. France 49 1411-1423
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  • One could expect |Ψ|2 = 1- Φ which expresses that the superfluid phase is pure 4He and the normal phase is pure 3He. However, the existence of boundaries, which influence the two order parameters in a different way (increase of the 4He concentration near the substrate due to zero point motion in presence of the substrate attracting Van der Waals potential but decrease of the superfluid order parameter due to proximity effects [16-18]), lead to the expectation that the relation |Ψ|2 = 1 - Φ does not hold in all regions of the film. As a consequence, the most natural step is to introduce an additional energy associated with the mismatch 1 - Φ - |Ψ|2 which is generically a quadratic term of the form 1/2. α {1- Φ - |Ψ|2 }2, where α is a rigidity constant. In the limit α → + ∞, one recovers |Ψ|2 = 1 - Φ. The choice of a finite α allows the two order parameters to decouple somewhat. Developing this quadratic energy, we obtain terms which can be incorporated in a redefinition of the free energy G (Φ, |Ψ|2), with in addition, the last term in the r.h.s. of equation (2) embodying the degree of coupling between the two order parameters. Note that the form Φ. |Ψ|2 of the coupling can also be viewed as resulting from a mass term associated with gradients of the superfluidity different from (h2/8 π2 m*2) and proportional to the 3He concentration (L. Peliti, private communication).
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