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Supporting Information
Electronic Structure of Quasi-free-standing Germanene on
Monolayer MX (M=Ga, In; X=S, Se, Te)
Zeyuan Ni1, Emi Minamitani1, Yasunobu Ando1, Watanabe Satoshi1,*
1Department of Materials Engineering, The University of Tokyo, Tokyo 113-8656, Japan
*Corresponding authors: zeyuan_ni@ cello.t.u-tokyo.ac.jp; [email protected]
AA-t
AA-b
AB-M-t
AB-M-b
AB-X-t
AB-X-b
(c)
Ge XM
(d)
(e)
(a)
(b)
AA-t AA-b AB-X-t AB-X-b AB-M-t AB-M-b0.00
0.02
0.04
0.06
0.08
0.10
0.12
Ene
rgy
Diff
eren
ce (e
V)
GaS GaSe GaTe InSe
(f)
Figure S0 (Figure 1, provided here for the convenience of reference): Top and side views of free
standing ML (a) MX and (b) germanene. (c) All the six high symmetric stacking configurations of
germanene on MX. (d) Side and (e) top views of 1 × 1 stacked ML germanene and MX with the most
preferable stacking. Thick dashed lines denote the lattice, and thin dashed lines denote the high
symmetric positions in hexagonal cells. M = Ga, In; X = S, Se, Te. (f) Energy difference between AB-
M-b configuration and the other configurations.
Electronic Supplementary Material (ESI) for Physical Chemistry Chemical Physics.This journal is © the Owner Societies 2015
-1 0 1-1135.595
-1135.590
-1135.585
-1135.580
-1135.575
-1135.570
-1135.565E
nerg
y (R
y)
Buckling (Ang)
E ~ 0.022 - 0.023 Ry ~ 0.3 eV
Figure S1: Total energy of germanene on GaTe with different buckling height. The whole system is
geometrically optimized while germanene is fixed. The left and right minimums correspond to AB-
M-t and AB-M-b configurations, respectively.
2.8 3.0 3.2 3.4 3.6 3.8 4.0-1135.595
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-1135.585
-1135.580
-1135.575
aa-b
ab-Ga-b
ab-Ga-t
ab-Te-b
ab-Te-t aa-t
Ene
rgy
(Ry)
Germanene-GaTe vertical distance (Å)
aa-t ab-Ga-b ab-Ga-t Optimized Stacking
Figure S2: Total energy of GaTe-germanene system with all 6 kinds of stacking. Stars denote the
energy given by geometry optimization. Lines denote the energy change by changing the vertical
distance between optimized and fixed germanene and GaTe.
-1 0 1 20.0
0.5
1.0
1.5
2.0
2.5
3.0
Y (R
elat
ive)
X (Relative)
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-1135.5902
-1135.5886
-1135.5870
-1135.5854
-1135.5838
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-1135.5807
-1135.5791
Energy
Figure S3: Energy map of germanene on GaTe with different lateral relative position while keeping
the vertical distance between germanene and GaTe. The configuration at X=Y=0 is the AB-M-b
configuration.
0 5 10 15 20 25-10
-8-6-4-202468
Har
tree
Pote
ntia
l (eV
)
Z (Å)
Dipole correctionSlope ~ - 0.03 eV/Å
(a) Potential
0 5 10 15 20 25-0.25
-0.20
-0.15
-0.10
-0.05
0.00
0.05
0.10
0.15
0.20
0.25
(b) Electric field
E (e
V/Å
)Z (Å)
GaS GaSe GaTe InSe
Dipole Correction Region
Figure S4: (a) Potential diagram averaged in the XY-plain along Z-direction of the germanene-GaTe
system. (b) Electric field diagram of averaged in the XY-plain along Z-direction of the germanene-
MX system. The electric field is the differential of the differential potential, i.e.
.dZ
PPPd MXgermaneneMXgermanene )(
(a) GaS (b) GaSe
(c) GaTe (d) InSe
(e) GaTe (top view)
Figure S5: Differential charge density of germanene-MX systems. Ge atoms are in the bottom part of
each figure and are colored in dark green. The isosurface is chosen as 0.0025. Red and green colors
indicate positive and negative values, respectively.
-3
-2
-1
0
1
2
3
-3
-2
-1
0
1
2
3 M K
Ene
rgy
(eV
)
All Germanene part
GaS GaSe
M K
GaTe
Ene
rgy
(eV
)
M K
InSe
M K
Figure S6: Band structure of Germanene-MX systems and the germanene parts only. The band
structure of the corresponding germanene part is calculated by simply removing the MX part to see
the effect of deformation on germanene.
-3
-2
-1
0
1
2
3
Ene
rgy
(eV
)
M K
Figure S7: Band structure of free-standing germanene calculated using the HSE functional. It is in
accordance with the HSE band structure given by Matthes et. al. (J. Phys.: Condens. Matter 2013, 25,
395305).
0 200 400 600 800 1000 1200
0
2
4
6
8
10
12
0 200 400 600 800 1000 1200
0
2
4
6
8
10
0 200 400 600 800 1000 1200
-0.5
0.0
0.5
1.0
1.5
2.0X
(Å)
steps
(a) (b)
Y (Å
)steps
(c)
Z (Å
)
steps
Figure S8: (a) X, (b) Y, and (c) Z positions of all Ge atoms at every step of molecular dynamics
simulation of germanene on GaTe at 500K. A 3 x 3 supercell is used in the simulation, so there are 18
Ge atoms in total. Dashed lines stands for those Ge atoms that start at a lower Z position (“bottom”
Ge), while solid lines for those at a higher Z position (“top” Ge). One step is 1.5 fs. Note that the X
and Y positions of Ge atoms oscillates around their initial positions, indicating a rather stable
configuration. On the other hand, the Z position of Ge atoms changes more greatly and sometimes
local flipping of “top” and “bottom” Ge happens. Although the non-local flipping (flipping of all “top”
and “bottom” Ge) is proved to have large energy barrier of 0.3 eV previously, local flipping engages
less atoms and experiences much lowered energy barrier, making it possible to happen. The molecular
dynamics simulation is performed by VASP in a 3 × 3 supercell under 500 K using the Nosé–Hoover
canonic thermostat.
-2
-1
0
1
2
Ener
gy (e
V)
Config 1 Ge projection
0.0000.20000.40000.60000.80001.000
M K
(a) (b)
Config 1 Ge p-orbital projection
0.0000.20000.40000.60000.80001.000
M K
(c)
Config 1 Config 2
M K
Figure S9: Band structure of germanene on GaTe during molecular dynamics (MD). (a) & (b) Band
structure of a random configuration during MD of germanene on GaTe with projection of (a) all
orbitals and (b) only p-orbital of Ge. The size of the dots indicates the absolute projection value and
the color indicates the percentage of the projection in total. (c) Band structure of two random
configurations during MD. Note that the MD is done in a 3 x 3 supercell, and the K point of the
primitive cell is folded to the Γ point in such a supercell. As we know, the Dirac cone of germanene
is mainly contributed by the p-orbitals of Ge atoms. Since the bands near the Fermi energy and the Γ
point in (b) are also mainly contributed by p-orbitals of Ge, we believe it is a deformed Dirac cone. In
addition, the MD is done at 500K, which should have overestimated the deformation of geometry and
probably the band structure compared with the case at room temperature. Last but not least, it is too
naïve using this MD result to interpret the electronic structure of germanene on MX at finite
temperature. They are only two transient configurations with little representativeness of the overall
property of germanene. Further study on the electron-phonon coupling of germanene on MX is
required to provide such overall electronic structure at finite temperature, but it’s beyond the scope of
this work.
Ge XM
-3
-2
-1
0
1
2
3
M K
Ene
rgy
(eV
)
Band Ge projection
0.0000.12500.25000.37500.50000.62500.75000.87501.000
Figure S10: Geometry and band structure of germanene on 3-layer InSe. The size of the dots indicates
the absolute value of Ge projection, and the color indicates the percentage of Ge projection in total.
Germanene has similar band structure as when it is on ML InSe.