Commensurate-incommensurate solid transition in the ${}^4$He monolayer on $\gamma$-graphyne

Abstract

Path-integral Monte Carlo calculations have been performed to study the ${}^4$He adsorption on $\gamma$-graphyne, a planar network of benzene rings connected by acetylene bonds. Assuming the ${}^4$He-substrate interaction described by a pairwise sum of empirical ${}^4$He-carbon interatomic potentials, we find that unlike $\alpha$-graphyne, a single sheet of $\gamma$-graphyne is not permeable to ${}^4$He atoms in spite of its large surface area. One-dimensional density distributions computed as a function of the distance from the graphyne surface reveal a layer-by-layer growth of ${}^4$He atoms. A partially-filled ${}^4$He monolayer is found to exhibit different commensurate solid structures depending on the helium coverage; it shows a C${}_{2/3}$ commensurate structure at an areal density of 0.0491Å${}^{-2}$, a C${}_{3/3}$ structure at 0.0736Å${}^{-2}$, and a C${}_{4/3}$ structure at 0.0982Å${}^{-2}$. While the promotion to the second layer starts beyond the C${}_{4/3}$ helium coverage, the first ${}^4$He layer is found to form an incommensurate triangular solid when compressed with the development of the second layer.

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Cited by in corpus (1)

• Efficient simulations of Hartree--Fock equations by an accelerated gradient descent method