Interlayer correlation between two 4He monolayers adsorbed on both sides of α-graphyne

Path-integral Monte Carlo calculations have been performed to study the He-4 adsorption on both sides of a single alpha-graphyne sheet. For investigation of the interlayer correlation between the upper and the lower monolayers of He-4 adatoms, the He-4-substrate interaction is described by the sum of the He-4-C interatomic pair potentials for which we use both Lennard-Jones and Yukawa-6 anisotropic potentials. When the lower He-4 layer is a C-4/3 commensurate solid, the upper-layer He-4 atoms are found to form a kagome lattice structure at a Mott-insulating density of 0.0706 angstrom(-2) and a commensurate solid at an areal density of 0.0941 angstrom(-2) for both substrate potentials. The correlation between upper- and lower-layer pseudospins, which were introduced in Kwon et al. [Phys. Rev. B 88, 201403(R) (2013)] for two degenerate configurations of three He-4 atoms in a hexagonal cell, depends on the substrate potential used; with the substrate potential based on the anisotropic Yukawa-6 pair potentials, the Ising pseudospins of both He-4 layers are found to be antiparallel to each other whereas the parallel and antiparallel pseudospin alignments between the two He-4 layers are nearly degenerate with the Lennard-Jones potentials. This is attributed to the difference in the interlayer distance, which is similar to 4 angstrom with the Yukawa-6 substrate potential but as large as similar to 4.8 angstrom with the Lennard-Jones potential.