Superfluidity of Atomically Layered ${}_{}{}^4{}_{}{}^{}He$ Films

The superfluidity of ${}^4\mathrm{He}$ films adsorbed on the atomically flat surface of graphite, preplated with HD to tune the surface binding potential, has been studied using a torsional oscillator. The superfluidity of a single uniform fluid layer of ${}^4\mathrm{He}$ shows an intrinsic coverage dependent suppression, while the fluid bilayer is fully superfluid at $T=0\mathrm{}$. The contribution of nonvortex excitations in the film to the normal density shows a strong dependence on coverage, arising from the atomic layering of the film.