Extremely High Frequency Dependence of Two-Dimensional Superfluid Onset

We observed the frequency dependence of the superfluid transition of 4 He films adsorbed on planar gold up to a very high frequency of 180 MHz, using the overtone harmonic modes of a quartz crystal microbalance. The superfluid onset was observed at a temperature markedly higher than the Kosterlitz–Thouless (KT) transition temperature, the onset temperature in the low-frequency limit. The observed frequency dependence is surprisingly well reproduced by the dynamic theory close to the high-frequency condition where the vortex diffusion length in a period becomes as small as the vortex core diameter. We also observed that the superfluid vortex parameters depend strongly on the kind of substrate as well as on 4 He film thickness.