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since the discovery of graphite as a homogeneous substrate for investigation of physisorbed monolayer films and various helium phases on it  @xcite , the most interesting question is whether he - he or he - c atomic interactions define helium behavior .
the study of adsorption of helium atoms on solid substrates therefore is important for both adsorption properties of surfaces and behavior of he atoms .
moreover , it was found that restricted geometry , such as nanoporous media or a two - dimensional substrate , provides new and unique features of helium .
for example , it was shown that in a porous medium a new helium phase appears  @xcite .
novel materials such as substrates can also lead to a new behavior of helium due to a different potential created by the substrate  @xcite .
it was shown that at certain densities and temperatures helium monolayers on graphene and graphite form commensurate and incommensurate solid phases and create a two - dimensional lattice  @xcite .
such structures were investigated previously  @xcite by quantum monte carlo ( qmc ) simulations . in the present work we have investigated the adsorption and stability of the first helium layers adsorbed on graphene by means of quasi harmonic approximation within density functional theory ( dft )  @xcite in order to examine the method .
investigations were then carried out on the new two - dimensional material s surface silicene in order to discover new possible adsorption properties of helium .
silicene is a graphene - like si - based material , which was first predicted theoretically  @xcite and then obtained experimentally  @xcite .
the electronic structure of this material is almost identical to graphene  @xcite but it exhibits a buckled surface and larger interatomic distance .
one can expect , therefore , that similar solid phases of helium on silicene will be expanded .
simulations of helium adsorption in different media such as a graphene nanotube  @xcite and a porous material called aerogel  @xcite within different variations of dft methods have recently been obtained .
all the results show that dft methods give an accurate description of the adsorption phenomenon .
moreover , it is known that among _ ab initio _ methods dft allows a balance to be achieved between computational cost and accuracy .
we started with the he - graphene system as a reference for verification of our simulation technique as there are a lot of experimental and theoretical data about adsorption and interaction of he atoms with graphene and graphite substrates  @xcite .
in addition , graphene and silicene both have similar structure and c and si atoms are isovalent .
the calculations were performed using dft method with gradient - corrected exchange , correlation energy functionals and projector augmented - wave method  @xcite implemented in vasp code  @xcite in medea @xcite program .
the maximum kinetic energy of plane waves in a basis set was equal to 480ev . to integrate in the brillouin zone we used
equidistant mokhorst - pack k - mesh @xmath0 centered at gamma point and methfessel - paxton @xcite smearing with the parameter 0.2ev .
optimization of the atomic positions was done by the conjugate gradient method with the maximal force equal to 0.005ev /  . in order to simulate the two - dimensional structure we added a 15  vacuum slab in the perpendicular to the surface direction .
we tested different computational approaches consisting of employing different types of exchange - correlation parts in the energy functional in order to better reproduce the he - graphene interaction potential .
we also checked the van der waals corrections due to the fact that at large distances , the he - substrate interaction is governed by van der waals interaction .
the obtained data was compared with the potential calculated by semiempirical method , based on the scattering of helium on graphite suggested in  ref.@xcite .
taking into account the van der waals corrections  @xcite is essential for correct reproduction of he - graphene interaction ( see fig.[fig : gr - he_interaction ] ) .
however , using such van der waals functionals as rev - pbe  @xcite , optb88 , optb86b  @xcite and optpbe leads to overestimation of potential well .
gga - pbe functional with semiempirical dft - d2  @xcite correction for long - range interaction reproduced the semiempirical data well and was chosen for further simulations .    to investigate the stability of the adsorbed helium monolayers we have calculated vibrational properties using medea - phonon module , which implements a direct approach of harmonic approximation  @xcite .
the so - called direct approach to lattice dynamics is based on the ab initio evaluation of forces on all atoms produced by a set of finite displacements of a few atoms within an otherwise perfect crystal .
the simulation model of silicene consists of one atomic layer of silicone atoms with crystallographic surface ( 001 ) of bulk silicone and space group symmetry @xmath1 .
the optimized hexagonal cell has a lattice size 3.85and interatomic distance @xmath2   ( close to @xmath3  @xcite and @xmath4  @xcite)and a buckling height @xmath5 .
we have calculated he - silicene interaction potentials in the perpendicular direction at various symmetric positions of he atom above the silicene surface .
[ fig : si - he_interaction](b ) demonstrates that the deepest potential well for helium is on the top of point s , corresponding to the center of the si hexagon .
the depth of the potential well for a helium atom is @xmath6 = 14mev and equilibrium height is @xmath7 = 3.20 .
the positions ah , al and sp of a helium atom have energy of about 4mev higher , which corresponds to 48k .
thus the position s is the most preferable adsorption site at low temperatures .
the interaction potential above the s point was approximated as a sum of pairwise lennard - jones ( lj ) interactions between he and each si atom in a range 10 .
lj parameters are @xmath8mev and @xmath9 3.6 .
we have computed a potential energy profile of a helium atom on the silicene surface along the lines shown in fig .
[ fig : si - he_interaction](a ) .
it can be seen in fig .
[ fig : si - he_interaction](d ) that the center of the hexagon ( s point ) represents a potential well for the helium atom as in the perpendicular direction .
( a ) , c@xmath10 ( b ) and c@xmath11 ( c ) helium phases on graphene and si@xmath12 ( d ) , si@xmath10 ( e ) and si@xmath11 ( f ) helium phases on silicene .
presence of imaginary modes indicates structural instability.,scaledwidth=70.0% ]    recent qmc calculations have shown that a helium monolayer adsorded on graphene at low temperatures could demonstrate different phases depending on helium coverage  @xcite . at low coverages
there is stable c@xmath12 commensurate solid phase , which is characterized by one he atom corresponding to three adsorption sites ( s points )  @xcite . at higher helium coverage range
the domain walls phase exists . at a certain he density value
the c@xmath10 commensurate solid phase occurs . with subsequent density increase ,
the incommensurate phases are formed . at even higher helium coverage
a second he layer should appear  @xcite .
we have investigated stability of an adsorbed helium monolayer on graphene in three different phases c@xmath12 , c@xmath10 and c@xmath11 ( with 0.063 , 0.083 , 0.19@xmath13 coverages respectively ) .
the presence of vibrational modes with imaginary frequencies usually point out the structural instability . in fig
[ fig : gr - he_dos ] the density of states of vibrational spectra are given .
as one can see , phase c@xmath12 does not have any imaginary modes ( see fig .
[ fig : gr - he_dos ] ( a ) ) , implying stability of adsorbed layer , whereas c@xmath10 and c@xmath11 phases are unstable ( fig .
[ fig : gr - he_dos](b ) and ( c ) ) .
however , qmc simulation demonstrates the stability of the c@xmath10 phase .
this discrepancy could be explained by the lack of he atom zero point motion in our approach , where this effect could stabilize the inplane motion .
imaginary modes for vibrations of helium in the c@xmath11 phase along @xmath14 direction indicates layer promotion because of high he - he atoms repulsion , which is agrees well agreed with qmc calculations .    in the case of helium on silicene
the same phases correspond to 0.026 , 0.034 , 0.078@xmath13 coverages respectively .
the simulations show its instability by the presence of imaginary modes for he atoms in @xmath15 plane ( fig .
[ fig : gr - he_dos](d - f ) ) .
it could be interpreted as the tendency of he atoms to group into small clusters with higher density because of the large si - si distance and less attractive he - silicene potential in comparison to graphene .
we have explored stability of adsorbed monoatomic layers of helium within born - oppenheimer ( bo ) approximation for graphene substrate and found that for low coverages there is conformity with qmc calculations .
as coverage is increased zero point effects become dominant and results of bo and qmc simulations differ .
however , bo calculation points to the formation of a second layer for high he coverage that correlates with qmc calculations .
the similar phases of helium on silicene substrate were found to be unstable .
the depth of the potential well for he atom on silicene is about 14mev compared to 24mev on graphene according to our calculations .
the equilibrium position of a he atom above these surfaces also differs  3.20  and 2.93  for silicene and graphene respectively .
one can conclude , therefore , that silicene is less attractive substrate for he atom adsorption than graphene .
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 .