He3inHe4films: Homogeneous two-dimensional behavior

Abstract

We report measurements and analysis of the heat capacity of ${}_{}{}^3{}_{}{}^{}\mathrm{He}$ in films of ${}_{}{}^4{}_{}{}^{}\mathrm{He}$. The data span a range of ${}_{}{}^3{}_{}{}^{}\mathrm{He}$ coverage from 0.03 to 1 atomic layer and ${}_{}{}^4{}_{}{}^{}\mathrm{He}$ film thickness from 10 to 45 Å. We find that for cases where the ${}_{}{}^3{}_{}{}^{}\mathrm{He}$ remains homogeneously spread out over the surface of the film, it acts like a two-dimensional gas of Fermi quasiparticles. To analyze our data, we use a model whereby the ${}_{}{}^3{}_{}{}^{}\mathrm{He}$ retains its two-dimensional degree of freedom along the surface, but is quantized in its motion perpendicular to the surface. For thin films, up to about 25 Å, a single excited state within the film is necessary to describe the data satisfactorily. For the thickest films, several excited states become necessary. Equivalently, in this case, one may assume a continuous three-dimensional spectrum. The results of our analysis show that the ${}_{}{}^3{}_{}{}^{}\mathrm{He}$ on these films behaves quite differently from ${}_{}{}^3{}_{}{}^{}\mathrm{He}$ at the surface of bulk ${}_{}{}^4{}_{}{}^{}\mathrm{He}$. The surface effective mass and excitation energy are functions of coverage and ${}_{}{}^4{}_{}{}^{}\mathrm{He}$ thickness. This suggests that the ${}_{}{}^3{}_{}{}^{}\mathrm{He}$ is highly interacting with the strength of the interaction being controlled by the thickness of the ${}_{}{}^4{}_{}{}^{}\mathrm{He}$. For the thinnest films we find that the excitation energy has a minimum as a function of coverage, at about 0.2 layer.