Precision specific-heat studies of thin superfluid films

We report precision specific-heat measurements for two-dimensional helium films in Anopore membranes and in Millipore filter paper. Above the transition temperature and for films less than a superfluid layer thick, we find a distinct specific-heat peak which can be understood in terms of the Kosterlitz-Thouless vortex unbinding mechanism. Although our results are well described by the planar theory, transition broadening becomes evident for thicker films.