A Study of the Superfluid Transition in Helium Films Adsorbed to a Rough CaF$_2$ Surface Over a Large Temperature Range

Rough two-dimensional substrates, such as thermally deposited CaF$_2$, have been shown to modify the experimental signatures of the superfluid transition in adsorbed thin helium films. Previous experiments have investigated a series of increasingly rough surfaces over a limited temperature range and found that the features at the superfluid transition become less defined as substrate roughness is increased. In this work we use a single rough CaF$_2$ substrate and study the superfluid transition in adsorbed helium films over a wide range of temperatures. Our results show that as the transition temperature increases the abrupt jump in superfluid density at the transition become less distinct. The changing characteristics of the transition on a single CaF$_2$ substrate with temperature suggest that the reduced observability of the transition on rough substrates cannot be explained entirely by simple surface geometry effects, such as tortuosity.