Superfluid Onset, Frequency Response, and Connectivity

A recent study of thin ${\mathrm{He}}^4$ films by Chester, Yang, and Stephens using a quartz-microbalance technique has shown frequency anomalies ascribed to the onset of superfluidity. The data imply that superfluid is present at thicknesses less than those at the anomalies. We propose a model involving surface heterogeneities to explain the results. Using the same model, it is possible to resolve several puzzles associated with other studies of onset, including the anomalous attenuation of third sound.