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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.

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Presentation on theme: "ARMENIA2010 Ab-initio calculations of electronic and optical properties of graphane and related 2-D systems Olivia Pulci European Theoretical Spectroscopy."— Presentation transcript:

1 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

2 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)

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

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 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

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

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

9 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

10 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

11 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

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

13 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

14 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)

15 Electronegativity plays a role!

16 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

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

18 Graphane HomoLumo+1 NFES Lumo Nearly free electron states

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

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

21 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

22 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

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 Germane Side view Germane Top view Germene Top view Germene Side view +H Not planar!!!  = 0.63  = 0.73 Å Å

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

26 NFES

27 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) NFESyes Affinity>>0~0.4 eV >>0

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

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

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

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

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

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 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

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

38

39 From Dirac’s equation: Si-C 1.79 Angstrom

40 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

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

42 Optical properties (DFT)

43 Optical properties

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

45

46

47 0-D 1-D 2-D 3-D Hamiltonian of N-electron system: Nanoclusters Nanowires Surfaces bulks Biological systems... not possible to solve it!

48 Silicongraphane sandwich geometry NFE state C side

49 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)

50 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)

51 ?????

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

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


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