  The low-temperature properties of one and two layers of parahydrogen adsorbed
on graphite are investigated theoretically through Quantum Monte Carlo
simulations. We adopt a microscopic model that explicitly includes the
corrugation of the substrate. We study the phase diagram of a monolayer up to
second layer promotion, and the possible occurrence of superfluidity in the
second layer. We obtain results down to a temperature as low as 8 mK. We find
second-layer promotion to occur at a considerably greater coverage than
obtained in previous calculations and estimated experimentally; moreover, we
find no evidence of a possible finite superfluid response in the second layer,
disproving recent theoretical predictions.
