Dimensionality effects in unsaturated helium-3, helium-4 and helium-3-helium-4 mixture films

he normal to superfluid transition in 2D is drastically different from that of bulk. The Kosterlitz-Thouless theory which describes the behavior of 2D films, predicts that the specific heat is regular at the transition followed by a maximum, due to the vortex-antivortex unbinding mechanism. The vortex-antivortex contribution to the specific heat has not yet been unambiguously observed in any experiment.;Using AC calorimetry, we performed a systematic specific heat study as a function of temperature and film thickness of helium films adsorbed in the cylindrical geometry of Anopore membranes. The 0.2 ;Three distinct regions of similar specific heat behavior, depending on thickness, were found. Films less than 2 atomic layers thick are characterized by a specific heat bump at a temperature that decreases with thickness. The bump disappears once the film is superfluid and a growing peak, shifting to higher temperatures with thickness is found. Upon increasing thickness, the peak contribution to the total specific heat decreases due to a fast growing regular background.;The thinnest films studied are strongly influenced by the underlying substrate adsorption potential. Results in this thickness regime are interpreted similarly to that in other porous materials.;The peak is interpreted in terms of the vortex-unbinding mechanism based upon fits to the planar theory, the influence of ;Films over 1 superfluid layer thick exhibit a break in the specific heat behavior, shifting to lower temperatures with thickness. This break indicates that new excitations due to the free surface and underlying adsorption potential become available. The films excitation spectrum is changing with thickness. The break stops at 0.38 K for films thicker than 50...