Prediction of stable C7/12 and metastable C4/7 commensurate solid phases for 4He on graphite

Using a substrate potential described by a pairwise sum of empirical He-4-C interatomic potentials, we have performed path-integral Monte Carlo calculations for He-4 adatoms on graphite. It is found that a second-layer commensurate structure is not stable above an incommensurate first-layer triangular solid. This is consistent with the conclusion of the previous theoretical study of Corboz et al. [Phys. Rev. B 78, 245414 (2008)] that was based on a laterally averaged one-dimensional potential. On the other hand, we observe a new stable C-7/12 commensurate solid in the first He-4 layer at the areal density of 0.111 angstrom(-2), which is close to the second-layer promotion density. This high-density commensurate solid exhibits a root 12 x root 12 structure registered to the graphite surface that is not disrupted by the development of the second He-4 layer. Furthermore, a second-layer 4/7 commensurate structure relative to the first-layer C-7/12 solid is found to be at least metastable, opening the possibility of two-dimensional supersolidity.