Abstract
Path-integral Monte Carlo calculations have been carried out to investigate physical properties of a $^{4}\mathrm{He}$ monolayer adsorbed on a single 6,6,12-graphyne sheet, which is one of the graphyne families possessing a rectangular symmetry. To characterize elusive quantum phases of an adsorbed $^{4}\mathrm{He}$ monolayer on 6,6,12-graphyne, we model the $^{4}\mathrm{He}$-graphyne interaction by the pairwise sum of empirical $^{4}\mathrm{He}\text{\ensuremath{-}}\mathrm{C}$ interatomic potentials. At partially filled $^{4}\mathrm{He}$ coverages, we identify three commensurate solids of the ${C}_{3/4},{C}_{4/4}$, and ${C}_{6/4}$ structures from the two-dimensional density distribution. These solids show the rectangular symmetry inherited from the symmetry of 6,6,12-graphyne, which were confirmed with the analysis of their static structure factors. At high helium coverages near its completion, the $^{4}\mathrm{He}$ monolayer is predicted to exhibit a transition from a rectangular commensurate structure to a triangular incommensurate structure, after going through inhomogeneous structures mixed with domains of triangular and rectangular orderings. This symmetry-changing transition has not been observed in $^{4}\mathrm{He}$ monolayers adsorbed on other carbon substrates.
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