graphene, graphane, graphene fluoride: materials for...

GraphEne, GraphAne, Graphene Fluoride:

Materials for Applications, Playground for Physicists

Jorge O. Sofo Department of Physics

and Materials Research Institute

Penn State



Jorge O. Sofo Department of Physics

and Materials Research Institute

Penn State

Alejandro Suarez

Ning Shen

Ajay Chaudhari

http://www.nsf.gov/index.jsp

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 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


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


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

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+

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.


No doping


0

Im 3

No doping


0

Im 3 c


0

Im 3 c

No doping T↑


0

Im 3 c

No doping T↓


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 [email protected]

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

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