Transcript hn - PLMCN10

Ab-initio calculations of electronic and
optical properties of graphane
and related 2-D systems
ARMENIA2010
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
[email protected]
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:
High 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)
E(eV)
Semi-metal
Functionalizing graphene
Graphene+H->Graphane
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
c
c
EXC
hn
hn
v
DFT
wcv
W
v
v
GW
BSE
Optical properties
ground state Band structure, I, A
TDDFT
AB-INITIO methods
MBPT
c
c
c
EXC
hn
hn
v
DFT
1)
wcv
W
v
v
GW
2)
TDDFT
BSE
3)
(Step 2)
Lars Hedin 1965
  iGW
G: single particle Green’s function
W: screened Coulomb interaction
W  V
1
For optical properties we need to go beyond:
Bethe Salpeter Equation
MBPT
c
c
c
EXC
hn
hn
v
DFT
1)
wcv
W
v
v
GW
2)
TDDFT
BSE
3)
Step 3: calculation of optical spectra within the
Bethe Salpeter Equation
c
hn
Absorption spectra
A photon excites an electron from an occupied
state to a conduction state
e
4
v
P  4PIQP  4PIQP
4
 4P
h
Bethe Salpeter Equation (BSE)
Kernel:   v  W
BSE
GW
e-h exchange
bound excitons
Ab-initio applicable to:
Biological systems
•Generality, transferability 0D-3D
•Detailed physical informations
•Predictivity
•Complex theory+large comp.cost
0-D
1-D
3-D
2-D
Nanowires
Nanoclusters
Surfaces
bulks
functionalizing graphene:
graphane
graphene
+ atomic H
Elias et al. Science 2009
Ryu et al. Nanolett. 2008
reversible!
Top view
Top view
sp  sp
2
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
A=electron affinity
I
A=E(vacuum)-E(CBM)
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
Egap DFT: 3.5eV
metallicmetal---> insulator transition
GW: 6.1 eV!!
A(DFT)=1.27 eV; A(GW)=0.4 eV >0!!
WHY??
+
_
dup
_
ddown
+
Side view
compensating dipoles
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
+H
Germene Top view
D= 0.63 Å
Germane Top view
D= 0.73 Å
Germene Side view
Germane 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?
graphene
Graphane
silicene
(H)
gap
no
yes G
Polysilane germene
(H)
Germane
(H)
yes GM no
yes G
DFT:3.5 eV
DFT:2.36 eV
DFT:1.34 eV
GW: 6.1 eV
GW:4.6 eV
GW:3.5 eV
no
No (0)
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
~0.4 eV >>0
>>0
>>0
>>0
Buckl
(Å)
Affinity >>0
OPTICAL PROPERTIES
Beyond single particle approach:
EXCITONIC EFFECTS
c
hn
v
Excitonic effects
Large Exciton binding energies!!! 2-D confinement + expected trend
Further possible (?) 2D materials
Si+C!!!!
SILICONGRAPHaNE SiC:H
SILICONGRAPHeNE SiC
Side view
Topview
SiC based 2-D
With H
GAP EXISTS!
On one side the affinity is smaller!!!
SiC:H
hn
e-
2 eV
hn
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
Research
Distribution:
ABINIT
FHI
OCTOPUS
Yambo
DP+EXC
TOSCA
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
Thank you for your attention
http://www.etsf.eu
[email protected]
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  V
1
Optical properties (DFT)
Optical properties
Comparison…
Large oscillators strength in Si and Ge-sheets!!!
Hamiltonian of N-electron system:
•Biological
systems
N
2
i
M
2
I
2
2
Zi Z j e2
p
P •...1not possible
e to solve it!Z i e
1
H 

 

 
2 i  j | ri  r j | i , j | r j  R i | 2 i  j | R i  R j |
i 1 2m
I 1 2M I
•0-D
•1-D
•2-D
•3-D
•Nanoclusters
• Nanowires
• Surfaces
•bulks
Silicongraphane
sandwich geometry
NFE state C side
H  E
• 1964: Density Functional Theory
E=E[n]
1998 Nobel Prize to Kohn
n
• Many Body Perturbation Theory
Green’s function method
GW + Bethe Salpeter Equation
(1965-->today)
• Time Dependent DFT (TDDFT)
(Gross 1984)
n(t)
G
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)
  0  Hartree
  iGVcoul  HartreeFock
 V
DFT
xc
 DFT KohnSham
????? ' GW' approx.
  iGW
(Hedin 1964)
Vertex function
Polarization
 Screened
 iGWCoulomb interaction
Self-Energy
G: single particle Green’s function
W: screened Coulomb interaction
W  V
1
Optical properties…
Large oscillators strength in Si and Ge-sheets!!!