Interlayer correlation between two $^4$He monolayers adsorbed on both sides of $\alpha$-graphyne

TL;DR

This study uses path-integral Monte Carlo simulations to explore how $^4$He monolayers on both sides of $\alpha$-graphyne interact, revealing substrate-dependent interlayer correlations and specific lattice structures at certain densities.

Contribution

It provides new insights into interlayer correlations of $^4$He on $\alpha$-graphyne, highlighting the influence of different substrate potentials on pseudospin alignments and layer structures.

Findings

Upper layer forms Kagomé lattice at certain densities.

Interlayer pseudospin alignment depends on substrate potential.

Different substrate potentials alter interlayer distance and correlation.

Abstract

Path-integral Monte Carlo calculations have been performed to study the $^4$He adsorption on both sides of a single $\alpha$-graphyne sheet. For investigation of the interlayer correlation between the upper and the lower monolayer of $^4$He adatoms, the $^4$He-substrate interaction is described by the sum of the $^4$He-C interatomic pair potentials, for which we use both Lennard-Jones and Yukawa-6 anisotropic potentials. When the lower $^4$He layer is a C$_{4/3}$ commensurate solid, the upper-layer $^4$He atoms are found to form a Kagom\'e lattice structure at a Mott insulating density of 0.0706 \AA$^{-2}$, and a commensurate solid at an areal density of 0.0941 \AA$^{-2}$ for both substrate potentials. The correlation between upper- and lower-layer pseudospins, which were introduced in Ref. [1] for two degenerate configurations of three $^4$He 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 pseudo-spins of both $^4$He layers are found to be anti-parallel to each other while the parallel and anti-parallel pseudo-spin alignments between the two $^4$He layers are nearly degenerate with the Lennard-Jones potentials. This is attributed to the difference in the interlayer distance, which is $\sim 4$ \AA~ with the Yukawa-6 substrate potential but as large as $\sim 4.8$ \AA~with the Lennard-Jones potential. [1] Y. Kwon, H. Shin, and H. Lee, Phys. Rev. B 88, 201403(R) (2013)