Band structure and thermodynamic properties of He atoms near a graphite surface

The energy-band structure and thermodynamic properties (in the noninteracting limit) of He atoms on graphite are calculated. Bound-state eigenvalues ${\epsilon }_n$ and matrix elements $〈n\left|V_{01}\right|n^{\prime }〉$ obtained in scattering experiments are used as input. The validity of the assumptions used to derive these quantities is verified for self-consistency. The results of these calculations differ from earlier studies in that the binding energies are 15 percent smaller and the corrugation is 50-100 percent larger. The effective mass enhancement $\frac{m^{*}}{m}$ is 1.06 for ${}_{}{}^4{}_{}{}^{}\mathrm{He}$ and 1.03 for ${}_{}{}^3{}_{}{}^{}\mathrm{He}$. Agreement with adsorption-isotherm determinations of the chemical potential in the limit of low coverage and temperature is remarkably good for both isotopes. These results, which are consistent with our previous analysis of the potential energy $V\left(\overrightarrow{\mathrm{r}}\right)$, indicate that band-structure effects cannot be neglected in treating He films on graphite.