Supersolidity in the second layer of $para$-H$_2$ adsorbed on graphite

We calculated the phase diagram of the second layer of $para$-H$_2$ adsorbed on graphite using quantum Monte Carlo methods. The second layer shows an incommensurate triangular crystal structure. By using a symmetric wave function, that makes possible molecule exchanges, we observed that this nearly two-dimensional crystal shows a finite superfluid density around a total density of 0.1650 \AA$^{-2}$. The superfluid fraction of this supersolid phase was found to be small, 0.41$\pm$0.05 \%, but still experimentally accessible.