Ab-initio calculations of electronic and optical properties of graphane and related 2-D systems
Olivia Pulci
European Theoretical Spectroscopy Facilty (ETSF), and CNR-INFM,
Dipartimento di Fisica Università di Roma Tor Vergata http://www.fisica.uniroma2.it/~cmtheo-group http://www.etsf.eu
olivia.pulci@roma2.infn.it

Everything started with graphene
Novoselov et al. Science 2004
•
3D: stacked in graphite
•
2D: graphene
•
1D: rolled in nanotubes
•
0D: wrapped in fullerens
•
Unique physical properties:
H igh carrier mobility
Ambipolar field effect
RT quantum Hall
Single molecule detection
Special mechanical properties
…………………
For a review see for example:
Castro et al. Rev. Mod. Phys. 81, 109 (2009)
Allen et al. Chem. Rev. 110, 132 (2010)

Semi-metal

OUTLINE

Ab-initio: Theoretical Approaches

Functionalizing Graphene with H: graphane

Other exotic 2D systems (Si, Ge, SiC)
 conclusions

OUTLINE

Ab-initio: Theoretical Approaches

Functionalizing Graphene with H: graphane

Other exotic 2D systems (Si, Ge, SiC)
 conclusions

AB-INITIO methods
MBPT c h n c h n
EXC w cv c
W v
DFT v GW ground state
Band structure, I, A v
BSE
Optical properties
TDDFT

AB-INITIO methods c v
DFT
1) h n v GW
2)
MBPT c h n
EXC w cv v
BSE
3) c
W
TDDFT

(Step 2)
Lars Hedin 1965
  iGW
G: single particle Green’s function
W: screened Coulomb interaction
W
  
1
V

For optical properties we need to go beyond:
Bethe Salpeter Equation c v
DFT
1) h n v GW
2)
MBPT c h n
EXC w cv v
BSE
3) c
W
TDDFT

h n
Step 3: calculation of optical spectra within the
Bethe Salpeter Equation c v
Absorption spectra
A photon excites an electron from an occupied state to a conduction state e
4
P
 4
P
IQP
 4
P
IQP
4  4
P h
Bethe Salpeter Equation ( BSE )
Kernel:
  v

W e-h exchange bound excitons

Biological systems
0-D
Nanoclusters
• Generality, transferability 0D-3D
• Detailed physical informations
• Predictivity
• Complex theory+large comp.cost
1-D
2-D
3-D
Nanowires
Surfaces bulks

functionalizing graphene: graphene graphane
+ atomic H
Elias et al. Science 2009
Ryu et al. Nanolett. 2008 reversible!
Top view
Top view sp
2  sp
3
1.42 A-> 1.52 A (like C bulk)
Side view
Theoretically predicted in 2007 (Sofo et al PRB2007), synthesized in 2008

Electron affinity
E(vacuum)
A
I
E
(CBM)
A=electron affinity
A=E
(vacuum)
-E
(CBM)
I=Ionization potential
I= E
(vacuum)
-E
(TVB)
Especially interesting when A<0
Technological applications (cold cathod emitters,…..)

C(111):H NEA
E(vacuum)
A
E
(CBM)
(1x1) bulk-like
No states into the gap
A=E
(vacuum)
-E
(CBM)
=-1.4 eV (GW) (-0.6 eV in DFT)
Exp :-1.27 eV (J.B. Cui et al PRL1998)

Electronegativity plays a role!

graphane graphene
A(DFT)=4.21 eV metallic Egap DFT: 3.5eV metal---> insulator transition
GW: 6.1 eV!!
A(DFT)=1.27 eV; A(GW)=0.4 eV >0!!

WHY??
Side view compensating dipoles
+
_
_
+ d up d down

Graphane
NFES
Homo
Lumo
Nearly free electron states
Lumo+1

Graphane: optical properties
DFT-RPA without H with H
Dramatic changes in the optical absorption spectrum!

Graphane optical properties: excitonic effects
From Cudazzo et al. PRL 104 226804 (2010)

Other exotic 2-d materials?

H
Graphene  graphane

H
Silicene(*) (?)  polysilane

H
Germene (?)  germane (?) polygermyne

……..?
22 toys models in Sahin et al. PRB2009
(*) Ag(110):Si Guy Le Lay and coworkers :
P. De Padova APL 2010
B. Aufray APL 2010

Silicon-based 2-D
+H
Polysilane top view
Silicene Top view
Silicene Side view
D
=0.44 Angstrom
Polysilane Side view
Not planar!!! Si larger atomic radii
D
=0.70 A

Si-based 2-D
Metallic!
Massless Dirac fermions at K
Wide gap semiconductor quasi-direct gap
DFT gap: 2.36 eV
GW gap: 4.6 eV

Ge-based 2-D
Germ e ne Top view
Germ e ne Side view
D
= 0.63
Å
+H
Germ a ne Top view
D
= 0.73
Å
Germ a ne Side view
Not planar!!!

Ge-sheets
Metallic!
Massless Dirac fermions at K semiconductor
Gap at
G:
DFT gap: 1.34 eV
GW gap: 3.55 eV

NFES

What can we learn?
gap
Buckl (Å) graphene Graphane no
No
(0) silicene Polysilane germene Germ a ne
(H) yes G no
(H) yes G
M no
(H) yes G
DFT:3.5 eV DFT:2.36 eV
GW:4.6 eV
DFT:1.34 eV
GW:3.5 eV GW: 6.1 eV yes
(0.46) yes
(0.44) yes
(0.70) yes
(0.63) yes
(0.73) sp2 sp3 sp3 sp3 sp3 sp3 d (Å) 1.42
1.54
2.28
2.39
2.35
2.39
NFES yes yes yes yes yes yes
Affinity >>0 ~0.4 eV >>0 >>0 >>0 >>0

OPTICAL PROPERTIES
Beyond single particle approach:
EXCITONIC EFFECTS c h n v

Excitonic effects
Large Exciton binding energies!!! 2-D confinement + expected trend

Further possible (?) 2D materials
Si+C!!!!
SILICONGRAPHeNE SiC
Side view
SILICONGRAPHaNE SiC:H
Topview

SiC based 2-D
With H
GAP EXISTS!
On one side the affinity is smaller!!!

SiC:H h n
2 eV e h n e -
Top and bottom semi-spaces have different ionization potential

Conclusions

H on graphene (graphane): metal->insulator transition; electron affinity decreases by factor 10

2-d systems (C, Si, Ge) show strong excitonic effects, with bound excitons

SiC:H presents 2 different ionization potentials!
(possible technological applications??)

Thanks to:

Paola Gori (CNR-ISM, Roma)

Margherita Marsili (Roma2)

Viviana Garbuio (Roma2)

Ari P. Seitsonen
(Zurich)



Friedhelm Bechstedt
(IFTO Jena, Germany)
Rodolfo Del Sole
(Roma2)
Antonio Cricenti
(CNR-ISM, Roma)

Development of theory training
Undergraduates
PhD Students
Post Docs
Other colleagues exp + Industry!
Development of codes
Distribution:
ABINIT
FHI
OCTOPUS
Yambo
DP+EXC
TOSCA
Research
Carrying on
Projects for users

BEAMLINES:
Optics
(O. Pulci)
EELS
(F. Sottile)
X-ray
(J. Rehr)
Transport
(P. Bokes)
Time-resolved excitations
(M.
Marques)
Photoemission (C. Verdozzi)
Raman
(G. Rignanese) new

Next call for projects: deadline 26 October
olivia.pulci@roma2.infn.it

From Dirac’s equation:
Si-C 1.79 Angstrom

BEAMLINES:
Optics
(O. Pulci)
EELS
(F. Sottile)
X-ray
(J. Rehr)
Transport
(P. Bokes)
Time-resolved excitations
(M.
Marques)
Photoemission (C. Verdozzi)
Raman
(G. Rignanese) new

(Step 2)
Lars Hedin 1965
  iGW
G: single particle Green’s function
W: screened Coulomb interaction
W
  
1
V

Optical properties (DFT)

Optical properties

Comparison…
Large oscillators strength in Si and Ge-sheets!!!

Hamiltonian of N-electron system:
•
Biological systems
H
 i
N 

1 p i
2
2 m

I
M 

1
P
I
2
2 M
I
 • ...
1
2 i

 j
| r i e

2 r j
|
 i ,
 j
| r
2 j
Z i
 e
R i
|

1
2 i

 j
|
Z i
Z
R i
 j e
2
R j
|
•
0-D
• 1-D
•
Nanoclusters
•
Nanowires
•
2-D
•
Surfaces
• 3-D
• bulks

Silicongraphane sandwich geometry
NFE state C side

H
 
E

•
1964: Density Functional Theory
E=E
[ n
] n
1998 Nobel Prize to Kohn
•
Many Body Perturbation Theory
Green’s function method
GW + Bethe Salpeter Equation
(1965-->today)
G
•
Time Dependent DFT (TDDFT)
(Gross 1984) n(t)
GROUND-STATE
EXCITED STATES

C(001):H NEA
E(vacuum)
A
E
(CBM)
Negative electron affinity
A=E
(vacuum)
-E
(CBM)
=-1.5 eV
(-0.7 eV in DFT)
Exp: -1.3
eV (F. Maier et al PRB2001)

 

  iGV coul




V xc
DFT

 iGW


(Hedin 1964)
Vertex function
Polarization
  iGW
Screened Coulomb interaction
Self-Energy
G: single particle Green’s function
W: screened Coulomb interaction
W
  
1
V

Optical properties…
Large oscillators strength in Si and Ge-sheets!!!