Critical Behavior of the Thermal Conductance ofHe3-He

Abstract

We report measurements of the connective conductance of 3 He-4 He films near the superfluid transition. This thermal response is tested for the critical behavior observed in pure 4 He films. We find that this is preserved for mixtures. The parameters 6 and D/a 2 , however, show a strong renormalization, and an unusual 3 He dependence. The conductance at fixed T-T c decreases upon addition of 3 He implying a decrease of the 2D correlation length. We observe a decrease in the maximum value of conductance which we attribute to a residual free-vortex density, even for T< T c .The superfluid transition of 4 He films when physisorbed on a two-dimensional (2D) substrate can be described by the vortex-antivortex unbinding theory of Kosterlitz and Thouless. 1 Measurements which yield the superfluid density-third sound, 2 " 5 quartz microbalance, 6 and torsional oscillator 3,7 -as well as experiments on thermal transport, 8 persistent currents, 9 and vortex diffusivity 10 have provided tests for the static and dynamic aspects of this theory. A first series of measurements on aspects of 2D to 3D crossover and the universal character of the transition as a function of film thickness have also been reported. 11 There is, in addition, in the case of liquid helium, the possibility to study the universal character of the transition in the presence of 3 He. Mixture films are, of course, the 2D analog of 3D mixtures; but, in fact, they are substantially richer in possibilities because of the important roles of the liquid-solid and liquid-vapor interfaces, and the arrangement of the 3 He relative to and along these interfaces. As regards the critical behavior, mixture films have been studied near the superfluid transition in several realizations: a submonolayer of 4 He and 3 He 12 ; multilayer films of 4 He with a more substantial amount of 3 He, concentrations up to 50% 13 ' 14 ; and a near monolayer of 4 He with a large amount of 3 He. 7 All of these realizations are of interest because, among other effects, the boundary conditions on the superfluid are quite different. In the first case one is dealing with a monolayer mixture bounded by a solid substrate on one side and effectively vacuum on the other. In the second case, larger amounts of 3 He and 4 He, one is dealing with what one may call a "slab" of a 3D mixture with the twist that the concentration is not quite uniform because of the underlying van der Waals field. In the last case one has a submonolayer mixture "sandwiched" between the solid substrate and a 3D-like layer of 3 He. There are aspects of these realizations having to do with location of the 3 He and 4 He, and possible mass rearrangement as the temperature is changed. Many of these questions are still not settled, and the extent to which they affect the critical behavior at the superfluid transition is not clear.The existing measurements with mixtures-mostly of the superfluid density-yield a picture of the transition which is qualitatively very similar to that of pure 4 He. The transition has the universal jum...