Universal behavior ofHe4films as a function of thickness near the Kosterlitz-Thouless transition

We report measurements of the convective conductance of ${}_{}{}^4{}_{}{}^{}\mathrm{He}$ films near the Kosterlitz-Thouless transition. Data for 14 films are analyzed over a range of critical temperatures from 1.28 to 2.16 K, and thicknesses 11.7 to 156 Å. We obtain good agreement using two different methods of analysis with the predicted behavior of the dynamic theory. The exponential divergence is observed up to six decades in conductance and one decade in reduced temperature. We find that the parameter b, which determines the sharpness of the divergence, and also the cusp in the superfluid density increases with film thickness. This is consistent with the growth of the three-dimensional correlation length. We find also that the ratio of diffusion constant to the square of the vortex core radius, D/${\mathit{a}}^2$, is a decreasing function of film thickness. We compare this with measurements in which D is obtained directly. We also report measurements of the nonlinear dependence of the conductance below the transition. These are shown to be consistent with measurements above the transition.