Sound Propagation and Transport Properties of Liquid 3 He in

Superfluid 3He confined in aerogel offers a unique chance to study the effects of a short mean free path on the properties of a well defined superfluid Fermi liquid with anisotropic pairing. Transport coefficients and collective excitations, e.g. longitudinal sound, are expected to react sensitively to a short mean free path and to offer the possibility for testing recently developed models for quasiparticle scattering at aerogel strands. Sound experiments, together with a theoretical analysis based on Fermi liquid theory for systems with short mean free paths, should give valuable insights into the interaction between superfluid 3He and aerogel. A model for liquid 3He in aerogel based on a random distribution of shortranged potentials acting on 3He quasiparticles has been shown to account semi-quantitatively for the reduction of the transition temperature, Tc, and the suppression of the superfluid density, ρs(T ). 1 Although the order parameter for 3He in aerogel is not firmly identified, measurements of the magnetization indicate that the low pressure phase is an ESP state.2 A transverse NMR shift is observed and is roughly consistent with that of an axial state even though the B-phase is stable in pure 3He at these pressures. The addition of a small concentration of 4He, which coats the aerogel strands, induces a suppression of the magnetization for T < T aerogel c , indicative of a non-ESP state like the BW phase.2 Thus, the stability of the superfluid state of 3He in aerogel is quite sensitive to the detailed interaction between 3He and the aerogel strands. Calculations of the free energy for 3He in aerogel which include anisotropic and magnetic scattering, and the effects of orientational correlations of the aerogel strands, confirm the sensitivity of the superfluid phases to the interaction between 3He and the aerogel.1,3 The high porosity of the aerogel implies that the silica structure does not significantly modify the bulk properties of normal 3He. The dominant effect of the aerogel structure is to scatter 3He quasiparticles moving at the Sound Propagation and Transport Properties of Liquid 3He in Aerogel 2 bulk Fermi velocity. If the coherence length, ξ0 = h̄vf/2πTc0, is sufficiently long compared to the average distance between scattering centers then a reasonable starting point is to treat the aerogel as a homogenous scattering medium (HSM) described by a mean-free path l.1 In this article we discuss the effects of a short mean free path on some of the transport properties of liquid 3He. The calculations presented below for sound propagation assume the BW phase is stable; however, the propagation and damping of lowfrequency sound are expected to be qualitatively similar for other phases. 0.0 0.5 1.0 1.5 T [mK] 0 10 20 30 P [b ar ] l = 140 nm l = 160 nm l = 180 nm l = 300 nm Tc (Bulk) Tc (Aerogel) Fig. 1 p-T phase diagram vs. l. The geometric mean-free path is estimated to be 1750 Å. The data is from Ref. 4. The superfluid transition temperature for 3He in aerogel is suppressed by quasiparticle scattering off the aerogel structure. In the HSM model the suppression of Tc is given by the Abrikosov-Gorkov formula,