Post on 13-Apr-2018
GraphEne, GraphAne, Graphene Fluoride:
Materials for Applications, Playground for Physicists
Jorge O. Sofo Department of Physics
and Materials Research Institute
Penn State
GraphEne, GraphAne, Graphene Fluoride:
Materials for Applications, Playground for Physicists
Jorge O. Sofo Department of Physics
and Materials Research Institute
Penn State
Alejandro Suarez
Ning Shen
Ajay Chaudhari
GraphEne, GraphAne, Graphene Fluoride:
Materials for Applications, Playground for Physicists
Co
urt
esy:
Ric
har
d K
aner
, UC
LA
Andre Geim
+ + =
A B A B A B
A B A B A B A B
A B A B A B A B
A B A B A B
A B A B A B A B
A B A B A B
A B A B A B
A B A B A B A B
A B A B A B
A B A B A B
A B A B A B A B
A B A B A B A B
A B A B A B
A B A B A B A B
A B A B A B
A B A B A B
A B A B A B A B
A B A B A B
A B A B
A A B
A B A B
A A B
A A B
A B A B
A A B
A B A B
A A B
A A B
1 1 2 2nR n a n a
1a
2a
A B A B
A A B
A B A B
A A B
A A B
1 1 2 2nR n a n a
1a
2a
B A
A B A B
A A B
A B A B
A A B
A A B
1 1 2 2nR n a n a
1a
2a
B A
,zn p nr A R r R
1 2,3zn p n
a ar B R r R
A B A B
A A B
A B A B
A A B
A A B
1 1 2 2nR n a n a
1a
2a
B A
,zn p nr A R r R
1 2,3zn p n
a ar B R r R
, ,n nB R A R
A B A B
A A B
A B A B
A A B
A A B
1 1 2 2nR n a n a
1a
2a
B A
,zn p nr A R r R
1 2,3zn p n
a ar B R r R
210 , .,, , ., ,n n
n
n nn n B R A R aH h cB R RB A A aR R
1, , with ,nik R
n
k
X R e X k X A BN
1, , with ,nik R
n
k
X R e X k X A BN
*
0 , , , ,k
H k A k B k k B k A k
1 21ik a ik a
k e e
1, , with ,nik R
n
k
X R e X k X A BN
*
0 , , , ,k
H k A k B k k B k A k
1 21ik a ik a
k e e
0
*
0
0k
k
1, , with ,nik R
n
k
X R e X k X A BN
*
0 , , , ,k
H k A k B k k B k A k
1 21ik a ik a
k e e
0
*
0
0k
k
0k k
1, , with ,nik R
n
k
X R e X k X A BN
*
0 , , , ,k
H k A k B k k B k A k
1 21ik a ik a
k e e
0
*
0
0k
k
0k k
ARPES Measurement (Aaron Bostwick and Eli Rotenberg, LBNL) 0 3 eV
q
K
xq
yq
q
Massless Dirac Fermions
0
*
0
0
0k
kH
k
q
K
xq
yq
qk K q
K q
0
F
0
30
2
30
2
q
q
i
qi
aq e
H v pa
q e
0F
3
2
aq q v q
2
2
1,
2
q
q
i
i
eq
e
0, !!, qq
Transport: Backscattering is suppressed
Carrier density controlled by gate voltage
(a) (b)
10 m
I
II
II
III
S D
G
Si
SiO2
Graphene
Cr/AuCr/Au
S D
G
Si
SiO2
Graphene
Cr/AuCr/Au
(a) (b)
10 m
I
II
II
III
S D
G
Si
SiO2
Graphene
Cr/AuCr/Au
S D
G
Si
SiO2
Graphene
Cr/AuCr/Au
A. Geim and K. Novoselov. “The rise of graphene.” Nat Mater 6, 183 (2007)
Hugo Romero, et al., ACS Nano (September 30, 2008).
Graphics courtesy of Kostya Novoselov
Cutting One Edge
Young-Woo Son, Marvin L. Cohen, and Steven G. Louie, “Half-metallic graphene nanoribbons,” Nature 444, 347 (2006)
DFT Calculations
Graphics courtesy of Kostya Novoselov
Graphics courtesy of Kostya Novoselov
CH Graphane Predicted by
JOS, A. Chaudhari, and G. Barber PRB 75,153401 (2007) Some evidence shown by
D. C. Elias, et al. Science 323, 610 (2009)
CF Carbon Monofluoride Discovered by
O. Ruff and O. BretshneiderZ. Anorg. Allg. Chem. 217, 1 (1934)
SiH Polysilane Predicted by
K. Takeda and K. Shiraishi, PRB 39, 11028 (1989) Synthesized by
J. Dahn, B. Way, E. Fuller, and J. Tse PRB 48, 17872 (1993)
Young-Woo Son, Marvin L. Cohen, and Steven G. Louie, “Half-metallic graphene nanoribbons,” Nature 444, 347 (2006)
2
eff2
kk
m
Compund CF CH (Graphane) Graphene
Electron Affinity (eV) 4.82 1.00 4.60
Ionization Potential (eV) 7.92 4.68 4.60
0.7 0.8 0.9 1.0k
0.3
0.2
0.1
0.1
0.2
0.3k
- +
- +
Energy shift -0.5 eV independent of the size of the channel or the barrier
IT IS CARBON AND HYDROGEN… CAN IT BE REALLY MAGNETIC?
H on Graphene
-0.1
6E-16
0.1
0.2
0.3
0.4
0.5
0.6
1 1.5 2 2.5 3
d_p
(Å
)
d(Å)
-0.8
-0.6
-0.4
-0.2
0
0.2
0.4
1 1.5 2 2.5 3
E_b
d (Å)
Relaxed
Fixed
d_p
d
F or H
F or H C
F or H C Δ
1 2 3
1
3c c c
F or H C Δ ΣΔ
1 2 3
1
3c c c
F or H C Δ ΣΔ
1 2 3
1
3c c c
2
0
3t
0
0
1
G
F or H C Δ ΣΔ
1 2 3
1
3c c c
2
0
3t
2
00
Im 3Im 3t G
F or H C
+
-
Δ ΣΔ
Σ+
Σ+
F or H C
+
-
Δ ΣΔ
Σ+
Σ+
2 2
3 31 1 1
1
3
i i
c e c e c
2 2
3 31 1 1
1
3
i i
c e c e c
0
3 1
2 2G G G
1
G
F or H C
+
-
Δ ΣΔ
Σ+
Σ+
1
0
0 0 0
3 0 0
0 3 0 0
0 0 0 0
0 0 0 0
H V
V t
G t
F or H C
+
-
Δ ΣΔ
Σ+
Σ+
F or H C
+
-
Δ ΣΔ
Σ+
Σ+
F or H C
+
-
Δ ΣΔ
Σ+
Σ+
1
0 0,
,
,
,
0 0 0
3 0 0
0 3 0 0
0 0 0 0
0 0 0 0
H HH
C
Un V
V Un t
G t Un
Un
Un
Hartree-Fock approximation
“Electrical Control of Chemical Bonding of Fluorine on Graphene” J. O. Sofo, A. M. Suarez, G. Usaj, S. Cornaglia, A. D. Hernandez-Nieves, C. A. Balseiro PRB 85, 115405 (2012)
F or H C
+
-
Δ ΣΔ
Σ+
Σ+
Beyond Hartree-Fock
F or H C
+
-
Δ
Beyond Hartree-Fock
F or H C
+
-
Δ
Beyond Hartree-Fock: Exact Diagonalization of small cluster
Beyond Hartree-Fock: Exact Diagonalization of small cluster
F or H C
+
-
Δ ΣΔ
Σ+
Σ+
Beyond Hartree-Fock: NRG
For details on the method see: Cornaglia et al. Physical Review Letters 102 046801 (2009) and references therein.
Beyond Hartree-Fock: NRG
No doping
Beyond Hartree-Fock: NRG
0
Im 3
No doping
Beyond Hartree-Fock: NRG
Beyond Hartree-Fock: NRG
0
Im 3 c
Beyond Hartree-Fock: NRG
0
Im 3 c
No doping T↑
Beyond Hartree-Fock: NRG
0
Im 3 c
No doping T↓
Beyond Hartree-Fock: NRG
0
Im 3
with doping
EXPERIMENT<-> SIMULATION<->THEORY A final comment:
Simulations describe complexity. Our theoretical work is to make it simple.
Thank you! Jorge Sofo sofo@psu.edu
1. N DOPED OR P DOPED? Now the “potpourri “ of results
Surf
ace
stat
es
Experimental Setup Peter Eklund, Hugo Romero, Prasoon Joshi, Humberto R. Gutierrez, Srinivas A. Tadigadapa
(a) (b)
10 m
I
II
II
III
S D
G
Si
SiO2
Graphene
Cr/AuCr/Au
S D
G
Si
SiO2
Graphene
Cr/AuCr/Au
(a) (b)
10 m
I
II
II
III
S D
G
Si
SiO2
Graphene
Cr/AuCr/Au
S D
G
Si
SiO2
Graphene
Cr/AuCr/Au
1.0
0.9
0.8
0.7
0.6
Rds/R
0 (
VD
irac
)
50403020100
t (hours)
T = 200°C
T = 25°C
(a)
120
80
40
0
-40
-80
VD
irac
(V
)50403020100
t (hours)
T = 200°C
T = 25°C
(b)
1.0
0.9
0.8
0.7
0.6
Rds/R
0 (
VD
irac
)
50403020100
t (hours)
T = 200°C
T = 25°C
(a)
120
80
40
0
-40
-80
VD
irac
(V
)50403020100
t (hours)
T = 200°C
T = 25°C
(b)
Vg
ΦS
P+ Si
W
M
ΦL
dL dS dR
WS
EL
ER
WS
WG
EG
ΦR
SiO2
Massless Dirac Fermions
0
*
0
0
0k
kH
k
q
K
xq
yq
qk K q
K q
0
0
30
2
30
2
q
q
i
qi
aq e
Ha
q e
0F
3
2
aq q v q
2
2
1,
2
q
q
i
i
eq
e
0, !!, qq
Transport: Backscattering is suppressed
Surface states Sub-1
Sub-2
Sub-3
From “The rise of graphene,” by A. K. Geim and K. S. Novoselov, Nat. Mat. 6, 183 (2007)
SLIDES PARA ARMAR Construction Zone
2. WANT OXYGEN MOVING FASTER? USE THE GATE VOLTAGE…
One more?
How does Oxygen diffuse across the surface?
95
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
Ene
rgy
Dif
fere
nce
(e
V)
Configurations
Barrier for oxygen diffusion is 0.73 eV
96
Carrier density controlled by gate voltage
(a) (b)
10 m
I
II
II
III
S D
G
Si
SiO2
Graphene
Cr/AuCr/Au
S D
G
Si
SiO2
Graphene
Cr/AuCr/Au
(a) (b)
10 m
I
II
II
III
S D
G
Si
SiO2
Graphene
Cr/AuCr/Au
S D
G
Si
SiO2
Graphene
Cr/AuCr/Au
A. Geim and K. Novoselov. “The rise of graphene.” Nat Mater 6, 183 (2007)
Hugo Romero, et al., ACS Nano (September 30, 2008).
Adding one electron lowers barrier to 0.13 eV
What happens when a charge is induced on the graphene lattice?
98
Removing one electron raises barrier to 0.89 eV
Effect on the Diffusivity
2/
04
BEk TdD ve
d=1.23 Å
1
0 26 THzv
2
0.73 eV (neutral)
0.13eV (n=-7.64E13 cm)E
16 2
6 2
Neutral Case: 5.410 cm/s
Doped Case: 3.010cm/s
D
D
10 orders of magnitude increase!
@ 300k
99 [1] G. H. Vineyard, J. Phys. Chem. Solids 3, 121 (1957).
2
[2] R.T. Yang and C. Wong, J. Chem. Phys. 75, 4471-4476 (1981).
A B A B A B
A B A B A B A B
A B A B A B A B
A B A B A B
A B A B A B A B
A B A B A B
A B A B A B
A B A B A B A B
A B A B A B
A B A B A B
A B A B A B A B
A B A B A B A B
A B A B A B
A B A B A B A B
A B A B A B
A B A B A B
A B A B A B A B
A B A B A B
A B
A B