H2 superglass on an amorphous carbon substrate

The phase diagram of a para-H2 monolayer absorbed on a experimentally syntetized amorphous carbon sheet was calculated using a diffusion Monte Carlo technique. We found that the ground state of that system changed drastically from a perfectly flat substrate to a situation in which the carbon atoms were allowed a certain degree of disorder in the $z$ direction. In the first case, at zero pressure we have a glass of density 0.056 $\pm$ 0.003 Å${}^{-2}$ in equilibrium with an incommensurate solid of 0.068 $\pm$ 0.002 Å${}^{-2}$. At the equilibrium density, the glass was found to have a tiny, but non-negligible superfluid faction of less than 1 % (0.44 $\pm$ 0.05 %). In the $z$-disordered substrate, we observe a significant enhancement of the superfluid fraction in the glass phase as well as a smaller but not zero value in the incommensurate crystal.