Stabilized silicene within bilayer graphene: A proposal based on molecular dynamics and density-functional tight-binding calculations
ABSTRACT Free standing silicene is predicted to display comparable electronic
properties as graphene. However, the yet synthesized silicene-like structures
have been only realized on different substrates which turned out to exhibit
versatile crystallographic structures that are very different from the
theoretically predicted buckled phase of freestanding silicene. This calls for
a different approach where silicene is stabilized using very weakly interacting
surfaces. We propose here a novel route by using graphene bilayer as a
scaffold. The confinement between the flat graphene layers results in a planar
clustering of Si atoms with small buckling, which is energetically unfavorable
in vacuum. Buckled hexagonal arrangement of Si atoms similar to free-standing
silicene is observed for large clusters, which, in contrast to Si atoms on
metallic surfaces, is only very weakly van der Waals coupled to the graphene
layers. These clusters are found to be stable well above room temperature. Our
findings, which are supported by density functional tight-binding calculations,
show that intercalating bilayer graphene with Si is a favorable route to
- SourceAvailable from: Mikhail I. Katsnelson[Show abstract] [Hide abstract]
ABSTRACT: Quantum electrodynamics (resulting from the merger of quantum mechanics and relativity theory) has provided a clear understanding of phenomena ranging from particle physics to cosmology and from astrophysics to quantum chemistry. The ideas underlying quantum electrodynamics also influence the theory of condensed matter, but quantum relativistic effects are usually minute in the known experimental systems that can be described accurately by the non-relativistic Schrödinger equation. Here we report an experimental study of a condensed-matter system (graphene, a single atomic layer of carbon) in which electron transport is essentially governed by Dirac's (relativistic) equation. The charge carriers in graphene mimic relativistic particles with zero rest mass and have an effective 'speed of light' c* approximately 10(6) m s(-1). Our study reveals a variety of unusual phenomena that are characteristic of two-dimensional Dirac fermions. In particular we have observed the following: first, graphene's conductivity never falls below a minimum value corresponding to the quantum unit of conductance, even when concentrations of charge carriers tend to zero; second, the integer quantum Hall effect in graphene is anomalous in that it occurs at half-integer filling factors; and third, the cyclotron mass m(c) of massless carriers in graphene is described by E = m(c)c*2. This two-dimensional system is not only interesting in itself but also allows access to the subtle and rich physics of quantum electrodynamics in a bench-top experiment.Nature 12/2005; 438(7065):197-200. · 38.60 Impact Factor
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ABSTRACT: Electronic and structural properties of a hypothetical material, silicon nanotubes, are examined through first-principles calculations based on density functional theory. Even considering that Si nanotubes have never been observed, this paper attempts to establish the theoretical similarities between Si and C, like band structures and density of states, as well as the main differences, especially associated with cohesive energies. The band-structure calculations for silicon nanotubes show that, similar to carbon structures, depending on their chiralities, they may present metallic (armchair) or semiconductor (zigzag and mixed) behaviors.Physical Review B 04/2000; 61(15). · 3.66 Impact Factor
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ABSTRACT: We report on the total-energy electronic-structure calculations on the basis of the density-functional theory that clarify atomic and electronic structures of the silicene on the Ag(111), the hexagonal BN, and the hydrogen-processed Si(111) surfaces. On the Ag(111) surfaces which are most commonly used as substrates for the silicene in current experiments, we find several stable and metastable structures with the 4×4, 13×13, and 23×23 periodicities with respect to the 1×1 Ag(111) lateral cell within the total-energy difference of 70 meV per Si atom. Those stable structures show the excellent agreement with the scanning tunneling microscopy measurement in their structural characteristics. The metastable structures with comparable total energies await experimental observations. In all the stable and metastable structures, the silicene is buckled substantially so that the π state rehybridizes with the σ state, leading to the π+ state, and then the linear energy dispersion peculiar to the Dirac electrons disappears in several cases associated with the opening of the energy gap. Moreover, we find that the substantial mixing of the π+ state, generated in such a way, with the states of the Ag atoms in the substrate converts the π+ state to the mixed π+ state and thus makes the state shift downwards or upwards, eventually annihilating Dirac electrons near the Fermi level. The absence of Dirac electrons caused in this way is found to be common to all the stable and metastable structures of the silicene on the Ag(111) substrates. We also find that the interaction between the π+ and the substrate orbitals should be weak enough to preserve Dirac electrons and at the same time be sizable to keep the system stable. We then propose two specific substrates as good candidates for the silicene with Dirac electrons, i.e., hexagonal BN and the hydrogen-processed Si(111) surface. We clarify that the silicene on those substrates are stable enough with the binding energy comparable to or twice that of the graphite and preserve Dirac electrons near the Fermi level.Physical Review B 06/2013; · 3.66 Impact Factor
Stabilized silicene within bilayer graphene: A proposal based on molecular dynamics
and density-functional tight-binding calculations
G. R. Berdiyorov,1,2M. Neek-Amal,2,3F. M. Peeters,2, ∗and Adri C. T. van Duin4
1Department of Physics, King Fahd University of Petroleum and Minerals, 31261 Dhahran, Saudi Arabia
2Departement Fysica, Universiteit Antwerpen, Groenenborgerlaan 171, B-2020 Antwerpen, Belgium
3Department of Physics, Shahid Rajaee Teacher Training University, Lavizan, Tehran 16785-136, Iran
4Department of Mechanical and Nuclear Engineering,
the Pennsylvania State University, University Park, PA 16802, USA
(Dated: January 15, 2014)
Free standing silicene is predicted to display comparable electronic properties as graphene. How-
ever, the yet synthesized silicene-like structures have been only realized on different substrates which
turned out to exhibit versatile crystallographic structures that are very different from the theoret-
ically predicted buckled phase of freestanding silicene. This calls for a different approach where
silicene is stabilized using very weakly interacting surfaces. We propose here a novel route by using
graphene bilayer as a scaffold. The confinement between the flat graphene layers results in a planar
clustering of Si atoms with small buckling, which is energetically unfavorable in vacuum. Buckled
hexagonal arrangement of Si atoms similar to free-standing silicene is observed for large clusters,
which, in contrast to Si atoms on metallic surfaces, is only very weakly van der Waals coupled to the
graphene layers. These clusters are found to be stable well above room temperature. Our findings,
which are supported by density functional tight-binding calculations, show that intercalating bilayer
graphene with Si is a favorable route to realize silicene.
The mechanical exfoliation of graphene1from graphite
has resulted in an enormous interest in this two-
dimensional monolayer of hexagonal ordered carbon
atoms which is due to its unique electronic, optical and
mechanical properties2that is expected to lead to po-
tential applications in different areas of electronics, opto-
electronics, etc. A material of even more current techno-
logical importance is silicon. It has been a longstanding
debate, dating back to the pioneering work of Yin and
Cohen,3whether or not graphitic Si is stable. Using pseu-
dopotential local-density-functional theory they doubted
that the formation of graphitic Si is possible because its
energy is 0.71 eV/atom higher than the diamond phase
and that a large negative pressure of -69 kbar is needed
to stabilize it. Even before the exfoliation of graphene in
2004 several theoretical works4,5have predicted that free-
standing single-layer silicon, called silicene,6–10is sta-
ble. Graphene’s sp2hybridization leads to a flat layer,
which in silicene is unfavorable with respect to a buck-
led Si(111) honeycomb structure with sp3hybridization.
The electronic structure has been shown to be similar to
graphene that is characterized by a zero gap and a Dirac
cone low energy spectrum. A unique feature of silicene
is its large spin-orbit interaction11that is predicted to
result in quantum spin Hall effect,12electrically tunable
band gap13and the emergence of a valley-polarized metal
Recently there has been very active experimental re-
search on the synthesis of silicene.
different silicene-like crystallographic structures were
obtained on different substrates, e.g.
A versatility of
Ir,17)depending on the growth conditions and the partic-
ular arrangement of the substrate atoms. These phases
were found to be different from the theoretical predicted
buckled configuration of freestanding silicene which are
a consequence of the interaction with the substrate and
the induced epitaxial strain. Furthermore, there is yet no
definite proof that these silicene like structures exhibit a
zero gap with a Dirac cone electronic spectrum.18–21Up
to now no freestanding silicene has been fabricated and
there is serious doubt that such a structure is even sta-
ble in nature. Here we propose that alternatively, one
can insert silicene between two substrates that interact
very weakly with the Si atoms, in order to stabilize it.
We show that once intercalated into the bilayer graphene
(either through domain boundaries or vacancy defects in
graphene layers23), the silicon atoms can be stabilized
to planar (with small buckling) silicon clusters during
thermal annealing, which can serve as building blocks
for a silicene sheet. It has been shown in recent density
functional theory (DFT) calculations that silicene layer
strengthens the interlayer binding between the graphene
sheets as compared to that in graphite without altering
the other properties of graphene like the Dirac fermion-
like electronic structure.22
In this work we conduct a systematic study of
the structural properties and the thermal stability of
Si atoms intercalating bilayer graphene using reac-
tive molecular dynamics (MD) simulations, which are
supported by density functional tight-binding theory
(DFTB).24–26We found that energetically unfavorable
planar silicon clusters in free space can be stabilized to
slightly buckled honeycomb structures by the weak con-
finement due to the induced straining in the graphene
arXiv:1401.3102v1 [cond-mat.mtrl-sci] 14 Jan 2014
are found to be different from those of silicene over
an Ag substrate27and are stable beyond room tem-
perature. At higher temperature they transit to three-
dimensional (3D) diamond-like structures with predomi-
nant sp3hybridization. Since such structures can natu-
rally arise during epitaxial growth of few-layer graphene
on bulk silicon carbide (SiC) by thermal decomposi-
tion28, our findings can be useful in the understanding
of the mechanisms for synthesis of multilayer graphene
on SiC.29–31The results may also initiate further re-
search on graphene-silicene superlattice structures with
promising structural and electronic properties. Recently,
it has been proposed32that analogous to graphene33hy-
drogenation of silicene clusters maybe a promising route
for hydrogen storage.
These quasi-two-dimensional (2D) Si clusters
To study the structural (thermal) properties of sil-
icene, MD simulations were performed using the reac-
tive force-field ReaxFF, which, in contrast to classical
force-fields, is a general bond-order dependent poten-
tial that accounts for bond breaking and bond forma-
tion during chemical reactions.34The system connec-
tivity is recalculated at every iteration step and non-
bounded interactions (van der Waals and Coulomb)
are calculated between all atom pairs, irrespective of
their connectivity.34–36Since ReaxFF parameters are de-
rived from quantum chemical calculations, it gives ener-
gies, transition states, reaction pathways and reactivity
trends in agreement with quantum mechanical calcula-
tions and experiments.34Numerical simulations are car-
ried out using the LAMMPS code37which includes the
ReaxFF method.38In order to have an independent test
of our used model we performed extra calculations using
We present now a systematic study of the structural
properties of Si atoms inserted between the graphene lay-
ers. Such intercalation can occur e.g. through domain
boundaries or defect areas in the graphene layer.23Here
we report only the energetically most favorable configura-
tions out of the many possible metastable configurations
(including 3D Si clusters) which we investigated. As a
representative example, we consider AB stacked bilayer
graphene (with 960 carbon atoms in each layer, corre-
sponding to a computational unit cell of 5.31×5.01 nm2
in the x − y-plane) with periodic boundary conditions
along the graphene basal planes in order to avoid edge
effects. The formation energies of Si clusters are calcu-
lated as:27Ef= (Et−N ×ESi−Eg)/N, where Etis the
total energy of the system, N is the number of atoms in
the cluster, ESi= 4.63 eV is the cohesive energy of Si,
layer graphene. (b-j) Ground state configurations [top (side)
view on the left (right)] of SiN clusters intercalating bilayer
graphene. The numbers show the formation energies in eV
per Si atom.
(color online) (a) A single Si atom on top of bi-
and Egis the energy of bilayer graphene.
We start by considering a single silicon atom adsorbed
on top of bilayer graphene, the equilibrium structure
of which is shown in Fig.
sorbed at bridge site forming a covalent bond (above the
middle of the carbon-carbon bonds) with bond distance
dSi−C = 2.08˚ A and formation energy of 1.1 eV. Such
bridge site attachment was recently predicted using first
principles calculations with binding energy of 1.17 eV and
Si-C distance in the range dSi−C= 2.04−2.11˚ A.39Si at-
tachment induces a small local change in the underlaying
planar graphene [see right panel of Fig. 1(a)] where the
carbon-carbon distance increases to 1.47˚ A, which is very
close to the DFT prediction (1.45˚ A).39This result is also
very different from the assumed hollow side positioning of
the Si atoms between graphene layers proposed in Ref.22.
Figure 1(b) shows the ground state configuration of the
system when the Si atom is inserted between the layers.
This Si atom is located at equal distance from both layers
and results in considerable local expansion and buckling
of the layers. The interlayer distance of bilayer graphene
without intercalating bilayer graphene is 3.29˚ A. The lo-
cal deformation of the graphene layers (in this particular
1(a). The Si atom is ad-
case about 50%) explains the considerable enhancement
of the formation energy as compared to the case when
the Si atom is adsorbed on top of bilayer graphene. Ef
decreases more than twice by the formation of a silicon
dimer [Fig. 1(c)], which is also located in the middle of
the interplanar spacing and weakly van der Waals bonded
with the graphene layers. A triangular cluster is found
in the ground state for N=3 as in the case of Si3 on
a metallic surface.27. All three Si atoms are located at
the center of the hexagonal ring of the lower graphene
layer and right below the carbon atom of the upper layer,
i.e., so called the “H-T” site [Fig. 1(d)].40Such energy-
minimum locations between the layers are observed for
larger Si clusters [see Figs. 1(e,f)]. Notice that line struc-
tures observed for free standing carbon clusters CNwith
N ≤ 5 (see e.g., Ref.41) are found to be metastable in case
of Si clusters. Figure 1(g) shows the equilibrium state
of Si6, which is the building block for silicene. Adding
one Si atom to it results in the Si7cluster which shows
(Fig. 1(h)) a planar ring structure with different Si in-
teratomic distances. The reason is that the Si atoms try
to accommodate the graphene matrix. The single ring
structure becomes energetically less stable with further
increasing N, and a double ring structure is found for
N = 8 and N = 9, as shown in Figs. 1(i,j). All the
considered ground state structures are planar except for
Si8and Si9, for which we observed a slight buckling (less
than 0.2˚ A). Note that the formation energy decreases
almost monotonically by increasing the number N of Si
atoms in the cluster. Thus, we found that the structure
of Si clusters inside bilayer graphene is totally different
from free standing Si clusters (see, e.g., Ref.42) and for
N >5 resembles (but are not identical) the ones observed
for carbon clusters in vacuum41.
In what follows, we study the structural properties of
SiNclusters consisting of six-membered silicon rings. Ini-
tial atomic configurations with a planar honeycomb ar-
gies (eV per Si atom) of Si clusters with six-membered rings
inside a bilayer graphene (graphene layers are not shown). (h)
Silicene sheet (160 Si atom computational unit cell) interca-
lating bilayer graphene.
(color online) (a-g) Geometries and formation ener-
rangement of Si atoms are used (see, e.g. Ref.27). Equi-
librium geometries and formation energies are shown in
Figs. 2(a-g) for N =6, 10, 13, 16, 19, 22 and 24. In-
terestingly, all the clusters retain their hexagonal ring
structure upon relaxation, whereas earlier work of Si on
metallic surfaces found that some of the clusters changes
its structure.27As in the case of smaller SiN clusters
(see Fig. 1), the Si atoms are not equidistant and the
buckling becomes more pronounced with increasing N.
However, the buckling is not constant across the cluster:
it is larger in the middle of the cluster and decreases to-
wards the edges. As in the case of metal supported Si
clusters27, the formation energy of SiNclusters decreases
as the cluster size increases.
Figure 2(h) shows the equilibrium structure of a sil-
icene sheet (with 160 Si atoms in the unit cell) interca-
lating bilayer graphene (360 C atoms in each layer of
the computational unit cell).
tions with a flat hexagonal arrangement of silicon atoms
– the state which was shown to be unstable in DFT
simulations.8The system transits to a buckled structure
upon energy minimization as shown in Fig. 2(h). In
the optimized geometry the averaged inter-atomic dis-
tance is around 2.24˚ A, which is close to the DFT pre-
dictions for silicene in vacuum (2.25˚ A).8The averaged
buckling parameter equals σ=0.65±0.07˚ A, which is com-
parable to the buckling of silicene on an Ag(111) surface
σ=0.85˚ A.27The distance between the graphene layers
is dG−G=6.92˚ A, which is almost twice larger than the
interlayer spacing in graphite. Such stacked structure of
planar graphene and buckled silicene layers has promis-
ing applications due to the fact that the properties of
both graphene and silicene remains unaltered, i.e. both
silicene and graphene exhibit a Dirac cone at the K-point
but with their respective Dirac points displaced energy.43
When studying larger size Si clusters inside bilayer
graphene (see Fig. 2), we have a predetermined hexago-
nal arrangement of Si atoms. However, in a real exper-
iments Si atoms may intercalate between the graphene
layers only at high temperatures (above 1000 K),30where
silicene is predicted to be unstable.8Thus the interesting
question in this case is what happens to the Si cluster
when temperature is rapidly quenched. To model this
situation, we conducted the following simulations: first,
we initialized the Si atoms randomly far from each other,
then increased temperature gradually (20 K/ps) from 0
to 2000 K. During this process Si atoms start migrat-
We started our simula-
layer graphene at different temperatures during a rapid cool-
(color online) Snapshots of Si18 cluster between bi-
view of the equilibrium structure of Si24 cluster intercalated
inside bilayer graphene with 960 carbon atoms in each layer.
(c) Optimized structure of Si24 cluster without graphene. (d)
Silicene sheet (160 Si atoms) intercalating bilayer graphene.
(color online) DFTB results: Top (a) and side (b)
ing (due to their small migration barrier40) and forms a
3D-like cluster at high temperatures, as shown in Fig.
3(a). After that we decreased the temperature with 20
K/ps. The cluster rearranges itself into different irregu-
lar shapes during this process [Figs. 3(b,c)]. At temper-
atures below 500 K the cluster is transformed into six-
member Si rings [Fig. 3(d)] and for lower temperatures
we observe the same planar cluster [with slight buckling,
see Fig. 3(e)] as we reported in Fig. 2. Animated online
video44shows such structural transformation. Note that
the formation of such Si cluster does not depend on the
rate of temperature increase/decrease. Thus, we predict
that planar Si clusters can be formed in real experiments
provided that Si atoms intercalate between the graphene
IV. DFTB CALCULATIONS
To support our findings about the stability of pla-
nar (with small buckling) Si clusters intercalated bilayer
graphene, we conducted simulations using DFTB theory,
which is approximately two orders of magnitude faster
than DFT and therefore enables one to model larger
systems.24–26As a typical example, we consider a Si24
cluster intercalating bilayer graphene with 960 carbon
atoms in each layer, i.e., the same system as in Fig. 2(g).
Figures 4(a,b) show the optimized structure of the sys-
tem, which shows the same buckled structure as found
in our MD simulations [see Fig. 2(g)]. Notice that we
started from a random distribution of Si atoms in a 2D
plane (see supplemental online video45).
librium state, the maximal buckling of the Si24 clus-
ter is σ = 0.719˚ A and the maximal deformation of
the graphene bilayer is 107%.
MD simulations for these parameters are σ = 0.715˚ A
and 103%.Note that such planar structures are not
even metastable in vacuum and transform spontaneously
into severely buckled configurations upon optimization,
In the equi-
The predictions of our
as shown in Fig.
calculations.27Figure 4(d) shows the optimized struc-
ture of silicene (160 Si atoms in the unit cell) intercalat-
ing bilayer graphene (360 carbon atoms in each layer),
i.e., the same system as in Fig. 2(h). Graphene layers
preserve their planar structure during optimization and
the buckling of the silicene layer is σ = 0.67 ± 0.05˚ A,
which is close to the predictions of our MD simulations
(σ = 0.65±0.07˚ A). Thus, DFTB simulations confirm in-
dependently the stability of the nearly planar honeycomb
arranged Si clusters intercalated bilayer graphene.
4(c), in accordance with our DFT
Finally, we consider the thermal stability of the
hexagon-based structures that we reported in Fig. 2.
Starting from the equilibrium state, we increased the
temperature of the system up to 2000 K at a rate
of 4 K/ps using an isothermalisobaric (NPT) ensemble
with a Nose-Hoover thermostat/barostat for tempera-
ture/pressure control.When the desired temperature
is reached, constant temperature MD simulations were
performed during 500 ps.46To characterize the thermal
stability of SiN clusters, we monitored the bond length
fluctuations given by the Lindemann index,
N − 1
i,j? − ?ri,j?2?
where N is the number of Si atoms in the cluster, δi
is the Lindemann index of atom i and δ is the Linde-
mann index for the entire cluster41. Figure 5 shows the
tercalating bilayer graphene as a function of temperature for
different N. Inset shows the melting temperature Tmof quasi-
2D SiN clusters constructed using the criterion δ = 0.1. Pan-
els 1-3 show snapshots of the SiN clusters at temperatures
indicated in the main panel indicated by filled symbols.
(color online) Lindemann index of SiN clusters in-
Lindemann index of Si6(circles), Si16(squares) and Si24
(triangles) clusters as a function of temperature. As a
general trend for small clusters (see e.g. Ref.36), δ in-
creases linearly with temperature for low temperatures.
A clear jump is observed in the δ(T) at higher temper-
atures, which corresponds to the formation of defects in
the honeycomb structure of Si atoms (see panels 1 and 2
of Fig. 5). With further increasing temperature a transi-
tion of quasi-planar silicon clusters into 3D-clusters is ob-
served (panel 3 of Fig. 5). Using the criterion of δ = 0.1,
we calculated the temperature Tmat which a structural
transformation of the silicene clusters into 3D-like clus-
ters takes place.The inset of Fig.
increases with increasing number of 6-member rings in
the system and that Tmtends to saturate around 1300 K
for larger N. In spite of the fact that free standing pla-
nar Si clusters are not stable [see Fig. 4(c)], here all the
quasi-2D clusters are found to be stable well above room
temperature, indicating the considerable contribution of
graphene layers to the stability of silicene Note, however,
that no structural transformation of the graphene ma-
trix is observed for the considered range of temperatures
(T ≤ 2000K) in our 500 ps-long simulations.
5 shows that Tm
Using reactive molecular dynamics and DFTB simula-
tions, we studied systematically the structural properties
and thermal stability of Si atoms intercalating bilayer
graphene. Due to the confinement from the graphene
layers, Si atoms form planar clusters, which are energet-
ically unfavorable for free standing Si clusters. Large Si
clusters form a buckled honeycomb structure resembling
the properties of free standing silicene predicted by first
principles calculations.8Our simulations show that sil-
icene intercalating graphene layers is much closer to pris-
tine silicene than silicene on metallic surfaces because of
the very small van der Waals interaction of graphene on
the silicene crystal structure. Therefore, graphene layers
are an almost ideal template for the formation of silicene.
Silicon clusters intercalating multilayers of graphene have
the potential for designing high-capacity energy storage
devices (see, e.g., Ref.47).
This work was supported by the Flemish Science Foun-
dation (FWO-Vl) and the Methusalem Foundation of the
Flemish Government. M.N.-A was supported by the EU-
Marie Curie IIF postdoc Fellowship/299855. One of us
(F.M.P.) acknowledges discussions with Prof. Hongjun
Gao. G.R.B acknowledges the support form the King
Fahd University of Petroleum and Minerals, Saudi Ara-
bia, under the TPRG131-CS-15 DSR project. A.C.T.vD
acknowledges funding from AFOSR grants FA9550-10-1-
0563 and FA9550-11-1-0158.
∗Electronic address: firstname.lastname@example.org
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44Supplimental online video: structural transformation of a
Si18 cluster intercalating bilayer graphene (with 1920 car-
bon atoms) when the temperature is decreased from 2000
K to 0.1 K with rate 20 K/ps in molecular dynamics sim-
45Supplemental online video: snapshots of a Si24 cluster in-
tercalating bilayer graphene (with 1920 carbon atoms) dur-
ing the DFTB optimization.
46The damping constants for temperature and pressure were
100 fs and 2 ps, respectively, and the time step was 0.5 fs
in all simulations.
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