Vortex dynamics in superfluid helium films

A high-Q torsional oscillator was used to measure the superfluid density and excess dissipation in thin films of ${}_{}{}^4{}_{}{}^{}\mathrm{He}$ as a function of temperature and film thickness. The effects of rotation on the Kosterlitz-Thouless transition were studied and the rotation-induced dissipation was measured. The first direct measurements of vortex diffusivity D as a function of the temperature through the superfluid transition were obtained. We find that D is a rapidly varying function of temperature in the vicinity of the transition. It is very small well below the transition, increases to order ħ/m at the static transition temperature, and appears to diverge at the point where the superfluid density vanishes. The diffusivity also appears to be insensitive to the presence of ${}_{}{}^3{}_{}{}^{}\mathrm{He}$ impurities and to the nature of the substrate.