ARMENIA2010

AR

ME

NIA

2010

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-grouphttp://www.fisica.uniroma2.it/~cmtheo-grouphttp://www.etsf.euhttp://www.etsf.eu

[email protected]

Everything started with graphene

•3D: stacked in graphite•2D: graphene•1D: rolled in nanotubes•0D: wrapped in fullerens

•Unique physical properties:High carrier mobilityAmbipolar field effectRT quantum HallSingle molecule detectionSpecial mechanical properties…………………

Novoselov et al. Science 2004

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

E(e

V)

Functionalizing grapheneGraphene+H->Graphane

OUTLINE

Ab-initio: Theoretical Approaches

Functionalizing Graphene with H: graphane

Other exotic 2D systems (Si, Ge, SiC)

conclusions

AB-INITIO methods

TDDFT

vv

DFT GW BSE

cc

h

c

h W

EXC

ground state Band structure, I, AOptical properties

MBPT

v

cv

AB-INITIO methods

TDDFT

vv

DFT GW BSE

cc

h

c

h W

EXC

1) 2) 3)

MBPT

v

cv

iGW

G: single particle Green’s function W: screened Coulomb interaction VW 1

(Step 2)Lars Hedin 1965

For optical properties we need to go beyond:Bethe Salpeter Equation

TDDFT

vv

DFT GW BSE

cc

h

c

h W

EXC

1) 2) 3)

MBPT

v

cv

Step 3: calculation of optical spectra within the

Bethe Salpeter EquationAbsorption spectra

A photon excites an electron from an occupied state to a conduction state

e

h

PPPP IQPIQP44444

Bethe Salpeter Equation (BSE)

GWBSE

Wv Kernel:

e-h exchange bound excitons

c

v

h

0-D 1-D 2-D3-D

Nanoclusters bulks

Biological systems

•Generality, transferability 0D-3D•Detailed physical informations•Predictivity

•Complex theory+large comp.cost

Ab-initioAb-initio applicable to:applicable to:

NanowiresSurfaces

functionalizing graphene:

Top view

Side view

Top view

32 spsp

+ atomic H

graphene graphane

Elias et al. Science 2009Ryu et al. Nanolett. 2008

reversible!

1.42 A-> 1.52 A (like C bulk)

Theoretically predicted in 2007 (Sofo et al PRB2007), synthesized in 2008

Electron affinity

A=electron affinity

A=E(vacuum)-E(CBM)

E(vacuum)

A

E(CBM)

Especially interesting when A<0 Technological applications (cold cathod emitters,…..)

I

I= E(vacuum)-E(TVB)

I=Ionization potential

C(111):H NEA

(1x1) bulk-likeNo 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)

E(vacuum)

AE(CBM)

Electronegativity plays a role!

graphane

A(DFT)=1.27 eV; A(GW)=0.4 eV >0!!

Egap DFT: 3.5eV GW: 6.1 eV!!

graphene

A(DFT)=4.21 eV

metallicmetal---> insulator transition

WHY??

Side view

dup

ddown

compensating dipoles

+

_

_

+

Graphane

Homo Lumo+1

NFES

Lumo

Nearly free electron states

Graphane: optical propertiesDFT-RPA

with H

without 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?

Graphene graphane

Silicene(*) (?) polysilane

Germene (?) germane (?) polygermyne

……..?(*) Ag(110):Si Guy Le Lay and coworkers : P. De Padova APL 2010 B. Aufray APL 2010

H

H

H

22 toys models in Sahin et al. PRB2009

Silicon-based 2-D

+HSilicene Top view

Silicene Side view Polysilane Side view

Polysilane top view

Not planar!!! Si larger atomic radii

=0.44 Angstrom=0.70 A

Si-based 2-D

Metallic! Wide gap semiconductorquasi-direct gapDFT gap: 2.36 eV GW gap: 4.6 eV

Massless Dirac fermions at K

Ge-based 2-D

Germane Side view

Germane Top viewGermene Top view

Germene Side view

+H

Not planar!!!

= 0.63 = 0.73Å Å

Ge-sheets

Gap at DFT gap: 1.34 eVGW gap: 3.55 eV

Metallic! semiconductor

Massless Dirac fermions at K

What can we learn?graphene Graphane

(H)

silicene Polysilane

(H)

germene Germane

(H)

gap no yes DFT:3.5 eV

GW: 6.1 eV

no yes M

DFT:2.36 eV

GW:4.6 eV

no yes DFT:1.34 eV

GW:3.5 eV

Buckl (Å) No (0)

sp2

yes (0.46)

sp3

yes (0.44)

sp3

yes (0.70)

sp3

yes (0.63)

sp3

yes (0.73)

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

Beyond single particle approach:EXCITONIC EFFECTS

c

v

h

OPTICAL PROPERTIES

Excitonic effects

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

Further possible (?) 2D materials

Side view

Topview

SILICONGRAPHaNE SiC:HSILICONGRAPHeNE SiC

Si+C!!!!

SiC based 2-D

On one side the affinity is smaller!!!

With H

GAP EXISTS!

SiC:H

Top and bottom semi-spaces have different ionization potential

h

h

e-

e-

2 eV

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)

Developmentof theory

training ResearchDevelopment of codes

UndergraduatesPhD StudentsPost DocsOther colleaguesexp + Industry!

Distribution:ABINITFHIOCTOPUSYamboDP+EXCTOSCA

Carrying onProjects 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

http://www.etsf.eu

Next call for projects: deadline 26 October

Thank you for your attention

[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

iGW


(Step 2)Lars Hedin 1965

Optical properties (DFT)

Optical properties

Comparison…

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

•0-D

•1-D •2-D•3-D

Hamiltonian of N-electron system:

•Nanoclusters• Nanowires • Surfaces

•bulks

•Biological systems

ji ji

ji

ji ij

iM

I ji jiI

IN

i

ieZZeZe

M

P

m

pH

||2

1

||||2

1

22

2

,

2

1

22

1

2

RRRrrr

•...not possible to solve it!

Silicongraphane

sandwich geometry

NFE state C side

EH

GROUND-STATE• 1964: Density Functional Theory

E=En 1998 Nobel Prize to Kohn n

EXCITED STATES

• Many Body Perturbation Theory Green’s function method GW + Bethe Salpeter Equation (1965-->today)

• Time Dependent DFT (TDDFT) (Gross 1984)

G

n(t)

C(001):H NEA

Negative electron affinity

A=E(vacuum)-E(CBM)=-1.5 eV (-0.7 eV in DFT)

E(vacuum)

A

E(CBM)

Exp: -1.3 eV (F. Maier et al PRB2001)

approx. GW''

ShamKohn DFT

Fock Hartree

Hartree 0

iGW

V

iGVDFT

xc

coul

?????

Vertex function

Polarization

Screened Coulomb interaction

Self-Energy

iGW

(Hedin 1964)


Optical properties…

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

ARMENIA2010

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