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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 Vergata http://www.fisica.uniroma2.it/~cmtheo-group

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ARMENIA2010

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  1. 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 ARMENIA2010

  2. 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)

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

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

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

  6. v v v TDDFT AB-INITIO methods MBPT c c EXC c hn wcv W hn BSE DFT GW Optical properties ground state Band structure, I, A

  7. MBPT c c EXC c hn wcv W hn v v v BSE DFT GW 2) 3) 1) TDDFT AB-INITIO methods

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

  9. MBPT c c EXC c hn wcv W hn v v v BSE DFT GW 2) 3) 1) TDDFT For optical properties we need to go beyond: Bethe Salpeter Equation

  10. c e hn h v GW BSE Kernel: 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 Bethe Salpeter Equation (BSE) e-h exchange bound excitons

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

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

  13. 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,…..)

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

  15. Electronegativity plays a role!

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

  17. WHY?? + dup ddown _ _ + Side view compensating dipoles

  18. Graphane NFES Lumo Homo Lumo+1 Nearly free electron states

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

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

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

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

  23. 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

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

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

  26. NFES

  27. What can we learn?

  28. Beyond single particle approach:EXCITONIC EFFECTS c hn v OPTICAL PROPERTIES

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

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

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

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

  33. 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??)

  34. 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)

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

  36. 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

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

  38. From Dirac’s equation: Si-C 1.79 Angstrom

  39. 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

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

  41. Optical properties (DFT)

  42. Optical properties

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

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

  45. Silicongraphane sandwich geometry NFE state C side

  46. 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) GROUND-STATE G EXCITED STATES n(t)

  47. 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)

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