Study of the Superfluid Transition in Two-Dimensional ${}_{}{}^4{}_{}{}^{}\mathrm{He}$ Films

We have studied the superfluid transition of a thin two-dimensional helium film adsorbed on an oscillating substrate. The superfluid mass and dissipation when analyzed in terms of the dynamic theory of Ambegaokar, Halperin, Nelson, and Siggia support the Kosterlitz-Thouless picture of the phase transition in a two-dimensional superfluid. The value for the jump in the superfluid density at the transition given by Kosterlitz and Thouless, ${\rho }_s\left({T_c}^{-}\right)=8\mathrm{}\pi k_{\mathrm{B}}{\left(\frac{m}{h}\right)}^2{T}_c$, is in good agreement with estimates from experiment.