Puzzling KT onset slope from third sound measurements with layered helium films on carbon nanotubes

Third sound measurements of thin ^$^4$He films adsorbed on multiwall carbon nanotubes 10 nm in diameter show layer-completion effects at 3, 4, and 5 atomic layers. Temperature sweeps at fixed film thickness show Kosteritz-Thouless onset behavior (a sudden rise in dissipation), but a puzzle is that the slope of the onset temperature with film thickness is only about 1/2 of the KT universal vaue. Speculation about the role of carbon-atom induced modulation of the film thickness will be discussed