Near-monolayer−43He films: Two superfluid transitions and theHe3effective mass and binding energy

We have measured the mass loading on a torsional oscillator of mixture films of ${}_{}{}^3{}_{}{}^{}\mathrm{He}$ and ${}_{}{}^4{}_{}{}^{}\mathrm{He}$ at coverages near one active atomic layer of ${}_{}{}^4{}_{}{}^{}\mathrm{He}$. These measurements yield information about the superfluid transition of ${}_{}{}^4{}_{}{}^{}\mathrm{He}$ and the effective mass and binding energy of ${}_{}{}^3{}_{}{}^{}\mathrm{He}$. Unlike the situation with submonolayer and multilayer films, where the superfluid transition takes place at a single temperature, we observe for these films a transition in two steps. This confirms a report some time ago of a similar observation by Bishop and Reppy. By comparing the mass loading at T=0 of pure ${}_{}{}^4{}_{}{}^{}\mathrm{He}$ films with that of mixtures, we obtain the ${}_{}{}^3{}_{}{}^{}\mathrm{He}$ effective mass which can be compared with results from the specific heat. We find, in particular, that the effective mass has a maximum as a function of ${}_{}{}^4{}_{}{}^{}\mathrm{He}$ thickness with correct asymptotic values for infinite and zero thickness limits. This maximum coincides very nearly with the thickness of ${}_{}{}^4{}_{}{}^{}\mathrm{He}$ at which the transition into the superfluid state takes place in two steps. In the submonolayer region the effective mass agrees with a density dependence one might expect as an extension of the theory of Pandharipande and Itoh for three-dimensional mixtures. We believe such theory should be able to be done for the two-dimensional case.