The phase diagram of a para-${\mathrm{H}}_2$ monolayer absorbed on an experimentally synthesized 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 $0.056\pm 0.003 {\text{Å}}^{-2}$ in equilibrium with an incommensurate solid of $0.068\pm 0.002 {\text{Å}}^{-2}$. At the equilibrium density, the glass was found to have a tiny, but non-negligible superfluid fraction 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.

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• Quantum fluids & solids
• 2-dimensional systems
• Monte Carlo methods