  Using quantum Monte Carlo we have studied the superfluid density of the first
layer of $^4$He and H$_2$ adsorbed on graphene and graphite. Our main focus has
been on the equilibrium ground state of the system, which corresponds to a
registered $\sqrt3 \times \sqrt3$ phase. The perfect solid phase of H$_2$ shows
no superfluid signal whereas $^4$He has a finite but small superfluid fraction
(0.67%). The introduction of vacancies in the crystal makes the superfluidity
increase, showing values as large as 14% in $^4$He without destroying the
spatial solid order.

Other Condensed Matter