Abstract
The behavior of a ${}^{4}\text{He}$ monolayer on a single graphene sheet in which the zero-point energy of the carbon atoms was taken into account was calculated. It was found that the ground state was a liquid of density $\ensuremath{\sim}$0.030 \AA{}${}^{\ensuremath{-}2}$, instead of the $\sqrt{3}\ifmmode\times\else\texttimes\fi{}\sqrt{3}$ commensurate arrangement found previously for flat graphene. Helium absorption on both sides of the carbon layer left the phase diagram unchanged with respect to the case in which only one of the two surfaces was available for coating.
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