  The study of the adsorption phenomenon of helium began many decades ago with
the discovery of graphite as a homogeneous substrate for investigation of
physically adsorbed monolayer films. In particular, helium monoatomic layers on
graphite were found to exhibit a very rich phase diagram.
  In the present work we have investigated the adsorption phenomenon of helium
atoms on graphene and silicene substrates by means of density functional theory
with Born-Oppenheimer approximation. Helium-substrate and helium-helium
interactions were considered from first principles. Vibrational properties of
adsorbed monolayers have been used to explore the stability of the system. This
approach reproduces results describing the stability of a helium monolayer on
graphene calculated by quantum Monte Carlo (QMC) simulations for low and high
coverage cases. However, for the moderate coverage value there is discrepancy
with QMC results due to the lack of helium zero point motion.
