Monolayer MX (M=Ga, In; X=S, Se, Te) Electronic Structure ... · Electronic Structure of Quasi-free-standing Germanene on Monolayer MX (M=Ga, In; X=S, Se, Te) ... c (e V) G a S G

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

-1135.590

-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)

-1135.5918

-1135.5902

-1135.5886

-1135.5870

-1135.5854

-1135.5838

-1135.5823

-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.