Zero-temperature phase diagram of D$_2$ physisorbed on graphane

We determined the zero-temperature phase diagram of D$_2$ physisorbed on graphane using the diffusion Monte Carlo method. The substrate used was C-graphane, an allotropic form of the compound that has been experimentally obtained through hydrogenation of graphene. We found that the ground state is the $\delta$ phase, a commensurate structure observed experimentally when D$_2$ is adsorbed on graphite, and not the registered $\sqrt 3 \times \sqrt 3$ structure characteristic of H$_2$ on the same substrate.