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ARMENIA2010 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 Vergatahttp://www.fisica.uniroma2.it/~cmtheo-grouphttp://www.etsf.eu olivia.pulci@roma2.infn.it

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Everything started with graphene 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 ………………… 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)

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Semi-metal E(eV) Functionalizing graphene Graphene+H->Graphane

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

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

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AB-INITIO methods TDDFT vv DFTGW BSE c c h c h W EXC ground state Band structure, I, A Optical properties MBPT v cv

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AB-INITIO methods TDDFT v v DFTGW BSE c c h c h W EXC 1) 2)3) MBPT v cv

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G: single particle Green’s function W: screened Coulomb interaction (Step 2) Lars Hedin 1965

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

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Step 3: calculation of optical spectra within the Bethe Salpeter Equation Absorption spectra A photon excites an electron from an occupied state to a conduction state e h Bethe Salpeter Equation (BSE) GW BSE Kernel: e-h exchange bound excitons c v h

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

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functionalizing graphene: Top view Side view Top view + atomic H graphene graphane Elias et al. Science 2009 Ryu 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

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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

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C(111):H NEA (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) E(vacuum) A E (CBM)

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Electronegativity plays a role!

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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 metallic metal---> insulator transition

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

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Graphane HomoLumo+1 NFES Lumo Nearly free electron states

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

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

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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

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

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

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Ge-based 2-D Germane Side view Germane Top view Germene Top view Germene Side view +H Not planar!!! = 0.63 = 0.73 Å Å

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

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NFES

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What can we learn? graphene Graphane (H) silicene Polysilane (H) germene Germane (H) gapno 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)1.421.542.282.392.352.39 NFESyes Affinity>>0~0.4 eV >>0

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

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

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

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

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

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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??)

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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)

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

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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

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http://www.etsf.eu Next call for projects: deadline 26 October Thank you for your attention olivia.pulci@roma2.infn.it

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From Dirac’s equation: Si-C 1.79 Angstrom

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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

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G: single particle Green’s function W: screened Coulomb interaction (Step 2) Lars Hedin 1965

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Optical properties (DFT)

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Optical properties

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

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0-D 1-D 2-D 3-D Hamiltonian of N-electron system: Nanoclusters Nanowires Surfaces bulks Biological systems... not possible to solve it!

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Silicongraphane sandwich geometry NFE state C side

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GROUND-STATE 1964: Density Functional Theory E=E n 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)

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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)

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?????

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Vertex function Polarization Screened Coulomb interaction Self-Energy (Hedin 1964) G: single particle Green’s function W: screened Coulomb interaction

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

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