PHYSICAL REVIEW B 87, 085423 (2013)
Adsorption of alkali, alkaline-earth, and 3d transition metal atoms on silicene
H. Sahin
*
and F. M. Peeters
†
Department of Physics, University of Antwerp, Groenenborgerlaan 171, B-2020 Antwerp, Belgium
(Received 30 August 2012; revised manuscript received 16 December 2012; published 19 February 2013)
The adsorption characteristics of alkali, alkaline-earth, and transition metal adatoms on silicene, a graphene-like
monolayer structure of silicon are analyzed by means of first-principles calculations. In contrast to graphene,
interaction between the metal atoms and the silicene surface is quite strong due to its highly reactive buckled
hexagonal structure. In addition to structural properties, we also calculate the electronic band dispersion, net
magnetic moment, charge transfer, work function, and dipole moment of the metal adsorbed silicene sheets.
Alkali metals, Li, Na, and K, adsorb to hollow sites without any lattice distortion. As a consequence of the
significant charge transfer from alkalis to silicene, metalization of silicene takes place. Trends directly related
to atomic size, adsorption height, work function, and dipole moment of the silicene/alkali adatom system are
also revealed. We found that the adsorption of alkaline-earth metals on silicene is entirely different from their
adsorption on graphene. The adsorption of Be, Mg, and Ca turns silicene into a narrow gap semiconductor.
Adsorption characteristics of eight transition metals Ti, V, Cr, Mn, Fe, Co, Mo, and W are also investigated. As
a result of their partially occupied d orbital, transition metals show diverse structural, electronic, and magnetic
properties. Upon the adsorption of transition metals, depending on the adatom type and atomic radius, the system
can exhibit metal, half-metal, and semiconducting behavior. For all metal adsorbates, the direction of the charge
transfer is from adsorbate to silicene, because of its high surface reactivity. Our results indicate that the reactive
crystal structure of silicene provides a rich playground for functionalization at nanoscale.
DOI: 10.1103/PhysRevB.87.085423 PACS number(s): 81.16.Pr, 73.22.Pr, 61.48.−c, 61.72.S−
I. INTRODUCTION
Recent advances in controllable synthesis and characteriza-
tion of nanoscale materials, have opened up important possibil-
ities for the investigation of ultrathin two-dimensional systems.
Chiefly the research efforts directed towards graphene
1,2
have
dominated the new era of two-dimensional materials. Many
exceptional features of atomically thin graphene layers such as
massless Dirac fermions, strength of the lattice structure, high
thermal conductivity, and half-integer Hall conductance have
been revealed so far.
3–6
In spite of its unique properties, due to
the lack of a band gap and its weak light adsorption, graphene
research efforts have focused on graphene composites over
the past five years. Studies have demonstrated the existence
of several chemically converted graphene structures such as
grapheneoxide (GO),
7–9
graphane (CH),
10–14
fluorographene
(CF),
15–19
and chlorographene (CCl).
20–22
The high-quality
insulating behavior, thermal stability, and extraordinary me-
chanical strength of fluorographene (CF) have inspired intense
research on halogenated graphene derivatives.
Unusual properties of graphene promising for a variety of
novel applications
23–28
have also triggered significant interest
in one or several atom-thick honeycomb structures of binary
compounds. Early experimental studies aiming to synthesize
and characterize novel monolayer materials have revealed
that graphene-like sheets of BN are also stable.
29–31
Though
BN has the same planar structure as graphene due to the
ionic character of B-N bonds, BN crystal is a wide band gap
insulator with an energy gap of 4.6 eV.
32–35
The perfect lattice
matching between graphene and BN layers make it possible
to construct nanoscale devices.
36
Following the synthesis of
hexagonal monolayer of ZnO,
37
the II-VI metal-oxide analog
of graphene, it was also predicted that ZnO nanoribbons have
ferromagnetic order in their ground state.
38
In addition to
these, it was reported that common solvents can be used to
exfoliate transition metal dichalcogenides and oxides such as
MoS
2
,WS
2
, MoSe
2
,MoTe
2
, TaSe
2
, NbSe
2
,NiTe
2
,Bi
2
Te
3
,
and NbSe
2
to obtain single layers.
39–41
Most recently, the
possibility of various combinations of MX
2
(M = transition
metal, X = chalcogen) type single-layer transition-metal
oxides and dichalcogenides, stable even in free-standing form,
was also predicted.
42
The recent synthesis of silicene,
43–45
the silicon analog of
graphene has opened a new avenue to nanoscale material
research. Though the nanotube
46
and fullerene
47
forms of
silicon were synthesized earlier, monolayer silicon was pre-
sumed not to exist in a freestanding form. Early theoretical
works pointed out that silicene is a semimetal with linearly
crossing bands and it has a buckled crystal structure that
stems from sp
3
hybridization.
48,49
Similar to graphene, the
hexagonal lattice symmetry of silicene exhibits a pair of
inequivalent valleys in the vicinity of the vertices of K and
K
symmetry points. Moreover, the experimental realization
of the transformation of thin films of wurtzite (WZ) materials
into the graphene-like thin film structure is another evidence
for the existence of monolayer structures of Si and Ge.
50
Recent theoretical studies have revealed several remarkable
features of silicene such as a large spin-orbit gap at the
Dirac point,
51
experimentally accessible quantum spin Hall
effect,
52
transition from a topological insulating phase to a
band insulator that can be induced by an electric field
53
and
electrically tunable band gap.
54
In addition to unique insulator
phases such as quantum spin Hall, quantum anomalous Hall,
and band insulator phases, the emergence of a valley-polarized
metal phase was also reported very recently.
55
It appears
that silicene will be a possible graphene replacement not
only due to its graphene-like features but also because of its
compatibility to existing silicon-based electronic devices.
In this paper, motivated by the very recent experimental
realizations of monolayer silicene,
43–45
we investigate how
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1098-0121/2013/87(8)/085423(9) ©2013 American Physical Society
H. SAHIN AND F. M. PEETERS PHYSICAL REVIEW B 87, 085423 (2013)
alkali, alkaline-earth, and transition metal atoms interact with
monolayer freestanding silicene. Details of computational
methodology are described in Sec. II. Characteristic properties
of monolayer silicene and graphene are compared briefly. Our
results on structural and electronic properties of metal adatom
adsorbed silicene are presented in Sec. IV. Conclusions and a
summary of our results are given in Sec. V.
II. COMPUTATIONAL METHODOLOGY
To investigate the adsorption characteristics of alkali metals
and transition metals on a monolayer honeycomb structure of
silicone we employ first-principles calculations
56
using the
projector augmented wave (PAW) method
57
implemented in
VASP code. Electronic exchange-correlation effects are simu-
lated using the spin-polarized local density approximation
58
(LDA). For the plane-wave basis set, the kinetic energy cutoff
is taken to be ¯h
2
|k + G|
2
/2m = 500 eV. Brillouin zone (BZ)
sampling is determined after extensive convergence analysis.
In the self-consistent potential, total energy, and binding
energy calculations with a (6×6×1) supercell of silicene sheet
a set of (5×5×1) k-point sampling is used for BZ integration.
For partial occupancies the Gaussian smearing method is used.
The convergence criterion of our self-consistent calculations
for ionic relaxations is 10
−5
eV between two consecutive steps.
By using the conjugate gradient method, all atomic positions
and the size of the unit cell were optimized until the atomic
forces were less than 0.05 eV
˚
A
−1
. Pressures on the lattice unit
cell are decreased to values less than 1 kB. Adatom adsorbed
silicene monolayers are treated using a supercell geometry,
where a minimum of 15
˚
A vacuum spacing is kept between
the adjacent silicene layers. Diffusion pathways of adatoms
are calculated for ten different adsorption points on (4×4×1)
silicene supercell.
The cohesive energy of silicene (also for graphene) per unit
cell relative to free Si atom, given in Table I, is obtained from
E
coh
= 2E
Si
T
− E
Silicene
T
, where E
Si
T
is the total energy of single
free Si and E
Silicene
T
is the total energy of silicene. Here, the total
energies of single atoms are calculated by considering their
magnetic ground state. As for the adsorption energy of a metal
adatom, one can use the formula E
Ads
= E
Ad
T
+ E
Silicene
T
−
E
Silicene+Ad
T
where E
Silicene
T
, E
Ad
T
, and E
Silicene+Ad
T
are the total
energies of the (6×6×1) supercell of silicene, isolated single
adatom, and silicene + adatom system, respectively.
Most of the adatom adsorption results in a net electrical-
dipole moment perpendicular to the plane. Therefore the
ground-state electronic structure, magnetic state, and work
function are calculated by applying a dipole correction
59
to
eliminate the artificial electrostatic field between the periodic
supercells. To obtain continuous density of states curves and
to determine the energy band gap (E
g
), smearing with 0.2
and 0.001 eV is used, respectively. For the charge transfer
analysis, the effective charge on the atoms is obtained by the
Bader method.
60
III. SILICENE
Though crystalline silicon has the diamond structure and no
layered form exists in nature, very recent experimental studies
have reported the successful synthesis of a monolayer of
silicon, called silicene, by the application of various deposition
(a) (b)
θ=116
o
d = 2.25 Α
Si-Si
o
δ = 0.49 Α
o
0
Energy (eV)
(c)
2
4
6
-2
-4
-6
ΓΚΜΜ
(VB) (CB)
ΓΓ
(VB) (CB)
ΚΚ
(VB) (CB)
ΜΜ
E
F
with SOC
without SOC
Δ
soc
1
.
5meV
FIG. 1. (Color online) (a) Top view of the honeycomb lattice of
silicene and its unit cell shown by a black parallelogram. (b) Tilted
view of the 2×2 supercell of silicene. Structural parameters: buckling
δ, Si-Si-Si angle, and Si-Si distance are indicated. (c) Electronic band
dispersion of silicene (with and without SOC) and band decomposed
charge densities of VB and CB at , M,andK symmetry points.
techniques. Similar to graphene, silicene can be viewed as a
bipartite lattice composed of two interpenetrating triangular
sublattices of silicon atoms. Since π bonds between silicon
atoms are weaker than in the case of the carbon atoms,
planarity is destabilized and therefore silicone atoms are
buckled in a silicene crystal. As shown in Fig. 1(b),the
buckling (perpendicular distance between these two Si planes)
is 0.49
˚
A. Upon the formation of sp
3
bonded honeycomb
lattice, the covalent bond length of Si-Si is 2.25
˚
A.
Two-dimensional silicene sheet is a semimetal because the
valence and conduction bands touch at the Fermi level. It
was predicted earlier that similar to graphene, silicene has also
linearly crossing bands at the K (and K
) symmetry points and
charge carriers in graphene behave like relativistic particles
with a conical energy spectrum with Fermi velocity V
F
∼
=
10
6
ms
−1
like in graphene.
48,49
In Fig. 1(c), the electronic
band structure of perfect silicene is presented. Linear π and
π
∗
bands that cross at the K symmetry point are responsible
for the existence of massless Dirac fermions in silicene.
Due to the degeneracy of the valence band (VB) maxima
and the conduction band (CB) minima at the K point, the
corresponding states have the same ionization potential and
electron affinity. Therefore one can expect the observation
of similar unique properties of graphene in silicene. The
calculated energy band gaps at M and symmetry points are
1.64 and 3.29 eV, respectively. At the point, the degenerate
085423-2
ADSORPTION OF ALKALI, ALKALINE-EARTH, AND 3 ... PHYSICAL REVIEW B 87, 085423 (2013)
TABLE I. Calculated values for graphene, and silicene. These are lattice constant (a), Si-Si (or C-C) bond distance (d), thickness of the
layer (t), work function (), cohesive energy per unit cell (E
coh
), in-plane stiffness (C), and optical phonon modes at the point.
Material a
˚
A d
˚
A δ
˚
A θ rad eV E
coh
eV C J/m
2
Phonons cm
−1
Graphene 2.46 1.42 ... 120 4.49 17.87 335
a
900–1600
Silicene 3.83 2.25 0.49 116 4.77 9.07 63
b
150–580
c
a
Reference 19.
b
Reference 62.
c
Reference 49.
VB is composed of p
x
and p
y
orbitals, while the CB is formed
by the hybridization of s and p
z
orbitals.
In Fig. 1(c), we also present the electronic band dispersion
taking into account spin-orbit coupling (SOC). Though clearly
the inclusion of spin-orbit interaction does not result in a
visible change in band dispersion, a band gap of = 1.5meV
appears at the K point. Due to its buckled structure, silicene
has a larger SO-induced gap than graphene, which is of the
order of 10
−3
meV.
61
The calculated band structure and band
gap opening () with SOC is in good agreement with recently
reported studies.
51,52,55
In Table I, we also compare structural, electronic, and
vibrational properties of graphene and silicene. It appears
that in contrast to the general trend, the larger the atomic
radius, the smaller the work function, silicene’s work function
is 4.77 eV, while for graphene it is 4.49 eV. The calculated
values of in-plane stiffness
62
and cohesive energy indicates
that silicene is a stable but less stiffer material as compared
to graphene. Similar to graphene’s out-of-plane optical (ZO)
phonon mode at 900 cm
−1
, silicene has a ZO mode at
150 cm
−1
. The eigenfrequencies of the LO and TO modes
are degenerate at the symmetry point and are found to be
580 cm
−1
, which is almost three times smaller than graphene’s
LO (and TO) modes.
IV. RESULTS: ADSORPTION OF METAL ATOMS
AsshowninFig.2, regarding the interaction of silicene
surface with adsorbates, four different adsorption positions
can be considered, i.e., above the center of hexagonal silicon
rings (hollow site), on top of the upper silicon atoms (top
site), on top of the lower silicon atoms (valley site), on top
of the Si-Si bond (bridge site). Considering the monolayer
Hollow
Top
Bridge
Valley
FIG. 2. (Color online) Preferable adsorption sites, hollow, top,
hill, and bridge, on a silicene lattice.
hexagonal lattice structure of silicene, it is reasonable to expect
the relaxation of foreign atoms to one of these adsorption sites.
A. Bonding geometry and migration barriers
We first investigate the adsorption characteristics of alkali
adatoms Li, Na, and K on silicene. The alkali metals are
highly reactive metals and their chemical activity increases
from Li to Fr. Characteristic bonding geometry of alkali atoms
is depicted in Fig. 3. Upon full geometry optimization, all
alkali atoms Li, Na, and K, favor bonding on the hollow
site of the silicene layer. The adsorption of alkali atoms
does not yield any significant distortion or stress on the
silicene lattice. The valley site on the low-lying silicon atoms
is the next favorable site. Though the top and valley site
adsorptions are also possible, bridge site adsorption of alkalis
is not possible on a silicene lattice. Therefore the bridge site
adsorption is a kind of transition state between top and valley
Li, Na & K Be & Mg
Ca, Ti, V, Mo & W Cr, Mn, Fe & Co
FIG. 3. (Color online) Side and top view for characteristic
adsorption geometries for alkali, alkaline-earth, and transition metal
atoms.
085423-3
H. SAHIN AND F. M. PEETERS PHYSICAL REVIEW B 87, 085423 (2013)
TABLE II. Calculated values for adatom adsorption on (6×6×1) silicene; relaxation sites hollow (H), bridge (B), valley (V) or top (T),
adatom height (h), adsorption energy of adatom (E
Ads
), total magnetic moment of the system (μ
tot
) in units of Bohr magneton (μ
B
), energy
band gap (E
g
), dipole moment (p), Bader charge transferred from adatom to silicene (ρ
ad
), and the work function of the optimized structure
(). Metallic and half-metallic structures are denoted as m and hm, respectively.
Site h (
˚
A) E
Ads
(eV) μ
iso
(μ
B
) μ
tot
(μ
B
) E
g
(eV) p (e
˚
A) ρ
ad
(e) (eV)
Li H 1.69 2.40 1.0 0.0 m 0.30 0.8 4.39
Na H 2.19 1.85 1.0 0.0 m 0.60 0.8 4.25
K H 2.70 2.11 1.0 0.0 m 0.94 0.8 4.09
Be V 0.78 2.87 0.0 0.0 0.39 0.00 1.3 4.68
Mg V 1.98 1.22 0.0 0.0 0.48 0.31 1.0 4.81
Ca B 1.49 2.68 0.0 0.0 0.17 0.62 1.3 4.47
Ti B 0.77 4.89 4.0 2.0 hm 0.29 0.9 4.77
V B 0.62 4.32 5.0 2.7 0.06 0.18 0.7 4.84
Cr H 0.48 3.20 6.0 4.0 hm 0.12 0.3 4.65
Mn H 1.04 3.48 5.0 3.0 0.24 0.10 0.4 4.73
Fe H 0.33 4.79 4.0 2.0 0.18 0.00 0.0 4.81
Co H 0.72 5.61 3.0 1.0 m 0.00 0.0 5.00
Mo B 0.37 5.46 6.0 0.0 m 0.15 0.1 4.97
W B 0.01 7.05 6.0 0.0 0.02 0.04 0.2 4.90
sites. Structural and electronic properties of alkali metals
adsorbed on silicene layer are also presented in Table II.
Here the height of adatoms is calculated as the difference
between the average coordinates of neighboring Si atoms and
the adsorbate. The distance between the adatom and silicene
surface monotonically increases with increasing atomic size.
However, fully conforming to graphene,
63
there is no clear
trend in the adsorption energies. While adsorption energies of
Li, Na, and K on graphene were calculated to be 1.1, 0.5, and
0.8 eV, respectively, their binding to silicene lattice is more
than twice stronger, i.e., 2.4, 1.9, and 2.1 eV, respectively. The
nature of the alkali-silicene bond will be discussed in the next
section.
Possible diffusion pathways of the adsorbate atoms on
silicene lattice can also be deduced from the energy barrier
between hollow, valley, top, and bridge sites. In Fig. 4,
we present the energetics of different adsorption sites. For
alkali atoms, shown in Fig. 4(a) it appears that the most
likely migration path between subsequent hollow sites passes
thorough the nearest valley sites. It is also seen that the energy
difference between hollow and valley sites becomes smaller
for larger atoms and therefore the diffusion of larger alkali
atoms is relatively easier. Though alkali atoms strongly bind
to the silicene surface, at high temperatures, they may diffuse
along hollow and valley sites when they overcome the energy
barrier of 140–280 meV.
Alkaline-earth metals are the elements of the periodic
table having two valence electrons in their outermost orbital.
Compared to alkalis, alkaline-earth metals have smaller atomic
size, higher melting point, higher ionization energy and larger
effective charge. Strong interaction between alkaline-earths
and silicon surfaces is well known and have been used for
various silicon etching and surface engineering techniques.
Therefore one can expect strong bonding of alkaline-earth’s to
a monolayer silicon surface. Resulting atomic geometries for
Be, Mg, and Ca adsorbed on a silicene sheet are depicted
in Fig. 3. Unlike alkalis, the hollow site is not the most
favorable adsorption site for alkaline-earth metals. Among
these, while Be and Mg favor adsorption to a valley site, the
Ca adsorbate that has a quite large atomic size (empirically
0
1
(a)
0
0.1
0.5
0.3
Bridge
Top Hollow
Li
Na
K
Energy (eV)
(b)
Energy (eV)
0
1.0
Energy (eV)
0.5
1.5
(c)
Be
Mg
Ca
Valley
Ti
V
Cr
Mn
Fe
Co
Mo
W
FIG. 4. (Color online) Diffusion pathways and barriers of (a)
alkali atoms and (b) 3d,4d,and5d transition metals through top,
bridge, valley, and hollow sites.
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ADSORPTION OF ALKALI, ALKALINE-EARTH, AND 3 ... PHYSICAL REVIEW B 87, 085423 (2013)
∼1.8
˚
A) prefers bridge site adsorption. The adsorption energy
of alkaline-earth’s is slightly higher for alkali metals (except
Mg). Similar to the Na adsorbate, a second row element,
the adsorption energy has a sharp decrease for the second
row alkali element Mg. As shown in Fig. 4(b), the Be atom
has to overcome a quite large energy barrier (E > 1eV)
for migration from valley to other adsorption sites. Sudden
increases in migration barrier stem from the stretching of
silicene lattice by the adsorbate, which is freed only in one
direction perpendicular to the surface. At high temperatures,
migration of Ca atoms through bridge and hollow sites may
take place by overcoming the energy barrier of 125 meV.
We next investigate the adsorption characteristics of eight
elements of the 3d,4d, and 5d transition metal adatoms:
Ti, V, Cr, Mn, Fe, Co, Mo, and W. Though the outermost s
orbitals of the transition metals are completely filled, because
of their partially filled inner d orbitals, diverse adsorption
characteristics for different atoms can be expected. Due to
relatively small atomic radius of all transition metals and
having more electrons that can participate in the chemical
bonding, we can expect stronger binding to the silicene lattice.
From Fig. 3, it appears that while the adsorption of alkalis
does not cause any significant change in the silicene lattice,
transition metals are more likely to disturb the nearest silicon
atoms.
Bonding of Ti adatom with 4.89 eV to silicene occurs
with a significant lattice distortion whereas the adsorption of
Ti occurs on the hollow site of graphene without disturbing
the planar lattice structure. As a consequence of bridge-site
adsorption of Ti, it binds six nearest Si atoms strongly by
pushing the underlying two Si atoms downwards. In order not
to exclude possible vacancy formation and adatom-induced
fracturing in such Ti-adsorbed silicene lattice, we also examine
the stability of the whole structure through molecular dynamics
(MD) calculations. Ab initio MD calculations show that the
adsorbed Ti atom remains bounded and neighboring Si-Si
bonds are not broken after ∼1 ps at 300 K. Similar to Ti, a V
adatom is adsorbed on a bridge site with 4.32 eV adsorption
energy.
Among the 3d transition metal adatoms considered here,
only Cr, Mn, Fe, and Co, similar to alkalis, are adsorbed on
the hollow site. However, differing from alkalis, transition
metals have quite strong binding (3.20, 3.48, 4.79, and 5.61
for Cr, Mn, Fe, and Co, respectively) with three uppermost
Si atoms. Therefore, instead of being adsorbed on top of a
hollow site like alkalis, transition metals are almost confined
in the silicene plane. Energetics of transition metal atoms on
the most favorable adsorption sites are also listed in Table II.
Note that not only the electronic occupancy but also the
atomic radius of the atom is important in determining the final
geometry of the adatom on silicene. Since for d orbitals having
more than half-occupancy the atomic radii are significantly
decreased by increasing the number of electrons, starting from
Cr all 3d transition metals prefer to be relaxed on a hollow site.
To see how the atomic radius of transition metal affects the
adsorption geometry, we also perform calculations for other
group VI elements Mo and W. According to the most recent
measurement of Cordero et al.,
66
the covalent atomic radii of
Cr, Mn, and W are 1.39, 1.54, and 1.62
˚
A, respectively. In this
column of the periodic table, while Cr is adsorbed on a hollow
site, bridge site adsorption becomes more preferable for Mo
and W due to their larger atomic radii. The effect of the atomic
radii can also be seen even in the same row elements: adatoms
Ti and V, which have a covalent radius larger than that of Cr,
are relaxed to the bridge site. Thus we can infer that only the
transition metal adatoms having covalent atomic radii larger
than ∼1.50
˚
A favor bridge site adsorption.
It appears from Fig. 4(c) that the energy barrier between
different adsorption sites is relatively large for transition metal
atoms. The diffusion barrier between the most favorable site
and the less favorable one is ∼0.6 eV. The most likely diffusion
path for Ti, V, Mo, and W passes from bridge to hollow sites.
However, diffusion of Mn, Cr, Fe, and Co atoms from one
hollow site to another one may occur via valley sites.
Furthermore, the effect of spin-orbit interaction on
the optimized adsorbate-silicene geometry is examined for
adsorption on (6×6×1) silicene supercell. Compared with the
optimized geometries obtained excluding SOC, SO-induced
change in adatom-silicon bond length is just on the order of
0.001
˚
A. It is also found that the migration path profile and
the most favorable adsorption site do not change when SOC is
included. Therefore, due to the negligible effect of spin-orbit
interaction on structural properties, in the rest of our study,
LDA calculations will be employed.
B. Electronic structure
In this section, we present spin-polarized electronic band
dispersion and density of states (DOS) for adatoms adsorbed
on the most favorable site on the silicene surface. Since the
alkaline-earth and transition metal adsorption significantly
disturb the hexagonal lattice symmetry, electronic band dis-
persion along the high symmetry points (-M-K-) of perfect
silicene may not represent the real electronic properties of the
whole structure. Therefore a density of states plot covering
large number of k points in the BZ is more convenient for a
reliable description of the electronic structure.
In Fig. 5, we present electronic band dispersions of alkali
metal adsorbed silicene. For the sake of comparison, the band
structure of the bare silicene is also included. Here, it is worth
Γ Μ Κ Γ Γ Μ Κ Γ Γ Μ Κ Γ Γ Μ Κ Γ
Silicene
Silicene+Li Silicene+KSilicene+Na
-0.5
-1.0
0.5
1.0
0
Energy (eV)
E = 0
g
E = 31 meV
g
E = 13 meV
g
E = 6 meV
g
FIG. 5. (Color online) Electronic band structures for perfect, Li,
Na, and K adsorbed silicene. Fermi level is set to zero. Occupied
bands are filled with yellow color.
085423-5
