Stability ofHe4superlattices on graphite

Using the variational method proposed by Lowy and Woo, we calculate the ground-state energies of the $\frac{1}{3}$- and ¼-coverage superlattices of ${}_{}{}^4{}_{}{}^{}\mathrm{He}$ physisorbed on graphite. The properly symmetrized single-particle factors in the trial wave function are constructed from expansions in an orthogonal basis set whose elements are the eigenfunctions of a Hamiltonian with a laterally averaged substrate potential. Calculation of the energy of the ${}_{}{}^4{}_{}{}^{}\mathrm{He}$ monolayer in the liquid phase is performed in a manner consistent with the superlattice calculation. The $\frac{1}{3}$-coverage coverage superlattice is found to be stable, while the ¼-coverage monolayer chooses to remain in the liquid phase.