Zero-temperature phase diagram of the second layer of $^{\bf 4}$He adsorbed on graphene

TL;DR

This study uses diffusion Monte Carlo simulations to map the zero-temperature phase diagram of $^4$He on graphene, revealing stable liquid and solid phases and their density limits, consistent with experimental data.

Contribution

First zero-temperature phase diagram of $^4$He on graphene, identifying stability limits of liquid and solid phases using advanced quantum Monte Carlo methods.

Findings

Stable liquid phase exists above 0.163 Å$^{-2}$ density.

Incommensurate solid phase appears above 0.186 Å$^{-2}$ density.

Metastability of 4/7 and 7/12 solids relative to incommensurate arrangements.

Abstract

The phase diagram at zero temperature of $^4$He adsorbed on an helium incommensurate triangular solid on top of a single graphene sheet has been obtained using the diffusion Monte Carlo method. We have found that, in accordance with previous experimental and simulation results for graphite, the ground state of $^4$He on this setup is a liquid that, upon compression, transforms into a triangular solid. To define the stability limits of both liquid and solid phases, we considered not only the adsorption energies of the atoms located on the second layer but the average energy of the atoms in both layers. Our results show that the lower density limit for a stable liquid in the second layer is 0.163 $\pm$ 0.005 \AA$^{-2}$ and that the lower limit for the existence of an incommensurate solid on the second layer is 0.186 $\pm$ 0.003 \AA$^{-2}$. Both values are in overall agreement with the results of torsional oscillator experiments and heat capacity measurements on graphite. The 4/7 and 7/12 registered solids are found to be metastable with respect to triangular incommensurate arrangements of the same density.