Universality of the Kosterlitz-Thouless transition in He4 films as a function of thickness

We report new measurements of thermal transport in He4 films near the superfluid transition. We have done this to check on the universality of this transition as a function of thickness or Tc between 1.37 and 1.88 K. Results from this study show for the first time a thickness or Tc dependence of the two characteristic parameters for the thermal conduction, the ratio of diffusion constant to vortex core radius, Da2, and the nonuniversal constant b. We suggest that the increase of b with film thickness is related to the bulk correlation length.