Superfluid transition ofHe4films adsorbed in porous materials

The superfluid transition of thin ${}_{}{}^4{}_{}{}^{}\mathrm{He}$ films adsorbed in ${\mathrm{Al}}_2$ ${\mathrm{O}}_3$ packed powders is studied using third-sound techniques. For powder grain sizes down to 500 Å, the transition is found to remain a Kosterlitz-Thouless vortex-screening transition. As the powder size is decreased, however, the drop to zero of the areal superfluid density becomes broadened, and the third-sound attenuation decreases. A finite-size model of the Kosterlitz-Thouless transition is formulated to explain these effects. Limiting the maximum vortex pair separation to the powder grain size leads to a broadening of the transition and reduced dissipation if the grain size is smaller than a vortex diffusion length. The model also describes many features of earlier measurements on films adsorbed in porous Vycor glass. The claim that the transition in Vycor films is three dimensional (not involving vortices) is reexamined in light of the present results.