Alejandro López Bezanilla

1. Effect of the Chemical Functionalization on Charge Transport in Carbon-based materials at the Mesoscopic Scale Alejandro López Bezanilla Institut des Nanosciences et Cryogénie (INAC) CEA Grenoble, France Examiners: · Prof. Mark Casida (UJF) Président du Jury · Prof. Juan José Sáenz (UAM) Rapporteur · Prof. Alain Rochefort (EPM) Rapporteur · Dr. Xavier Blase (CNRS) · Dr. Pablo Ordejón (CIN2) Encadrants: · Dr. Stephan Roche (CEA) Encadrant · Dr. Pascale Maldivi (CEA) Co-encadrante (Grenoble) · Dr. Vincent Derycke (CEA) Co-encadrant (Saclay)

2. ChimTronique Transversal axes Saclay (S. Palacin) Grenoble (R. Baptist)

3. Outline → Motivations →Electronic properties of CNTs and GNRs ·Functionalization →Decimation method ·Green´s function technique →Results · Functionalized nanotubes ·Functionalized nanoribbons ·Edge defects in nanoribbons

4. Carbon atom Carbon atom Hybrid Molecular Orbitals Cohesion Electronic properties in the vicinity of EF Valence electron orbitals: ~ 2D (sp2)‏ Graphene interactions between pz orbitals(bonds/bands)‏ ~ 3D (sp3)‏ Diamond

5. 2 1 1 2 2 1 1 1 2 atoms/ cell nearest neighbor orbital overlap 2 2 1 -effective model

6. EF Nanotubes electronic properties Periodic Boundary conditions Armchair Zigzag EF=0

7. Summarizing What would it happen if we alter these properties ?

8. Bio-, photo-sensors → Selectiveelectricalsignals of molecular adsorption events. → Protein interaction. → Virus detection. Zhou et al. Nano Letters 9, 1028 (2009)

9. e- Left lead Right lead 300 nm Bio-, photo-sensors Photoactive molecules: Phtalocyanine … →Transmission after photoactive molecule functionalization. → Properties of the linker. hv S. Campideli et al. J. Am. Chem. Soc. 2008, 130, 11503

10. Towards graphene nanoribbon transistor Using top-down lithography to fabricateGNRs… · Ribbons down to ~ 10 nm width P. Kim et al (Columbia Univ. USA) E. Dujardin (CEMES, France) Ph. Avouris et al. (IBM, USA) · MOSFETs : clean GNR-FET with ~ 3nm are necessary !!! W  2 nm ! X. Li et al., Science 319, 1229 (2008) X. Wang et al., PRL 100, 206803 (2008)

11. Functionalizing graphene 2D Graphene and Graphene ribbons Goal: how to create or enlarge energy/conduction band gaps A graphene-based electrochemical switch (M. Lemme & A. Geim)

12. Hybrid Carbon Based Materials Is sp2bonding broken/preserved?

13. sp3 sp2 sp2 vs sp3 functionalization CH2chemisoption Zigzag nanotube axis Armchair nanotube axis

14. sp3 sp2 vs sp3 functionalization Phenyl chemisoption Tube axis

15. sp3 sp2 Electronic states LDoS (0.6 eV) Energy bands 2 phenyls X Γ Γ X carbene 2 phenyls carbene

16. SIESTA: an ab initio approach →Efficient tool for first-principles calculations (geometrical relaxation,…) → Local atomic-like orbitals basis set: · no coupling beyond a cutoff distance, · sparse Hamiltonian. → No fittings, no adjustable parameters. sp-hybrid orbital p-orbital s-orbital

17. 1.3 nm Description of the system Building block →SWCNT (10,10) Size : ~ 500 atoms → phenyl groups 3 nm

18. Transport formalisms Kubo-Greenwood Landauer-Büttiker • Order N method : only Hamiltonian - Vector products allows big systems simulations • No contacts • Intrinsic properties • Quantum diffusion mechanism • Mean free path, scattering time, mobility • Order power N method : inversion of Hamiltonian limites size of systems simulations • Accuracy • Transmission and reflexion probability • Localization length, conductance

19. Problem statement Problemdefinition & Decimationtechnique

20. Problem definition Left lead Right lead Channel • Non-interacting electrons • Scattering free leads (perfect electrodes)‏ • No backscattering at lead - reservoir interface • Incident electrons are in thermal equilibrium with reservoirs

21. Problem definition Nanotubes Left lead Right lead channel Nanoribbons Left lead Right lead channel

22. (r) (a) T(E) = Tr [ ΓLGCΓRGC ] (r) (a) ΓL,R = i [ ΣL,R -ΣL,R ] ~ HC ΣL ΣR Conductance from Green´s function Fisher and Lee relation for transmission: where: ~ GC = [ E- HC - ΣL- ΣR ] - 1 S. Fisher and P.A. Lee, Phys. Rev. Lett., 23, 6851 (1981) Datta, Electronic transport in mesoscopic system, Cambidge (1995)

23. Channel Problem definition VLC VCR ... ... Left lead Right lead HL HL HR HR HC HC Semi-infinite leads + Long channel (~ 100.000 orbitals) HL 0 VLC VCL HC VCR H = VRC HR 0 Decimationtechniques Norb

24. Decimation: 2-site model Wavefunction: Hamiltonian: Eigenvalue equation: Energy spectrum: Eigenvalues:

25. Decimation: 2-site model Self-energy is an effective potential that corrects the non-interacting on-site energy

26. → A method to reduce the dimension of the Hamiltonian basis function space Decimation: 3-site model

27. ~ V1,4 ~ V4,1 ~ ~ H1 H4 Decimation: N-site model V2,3 V1,2 V3,4 H2 H3 H1 H4

28. Long channel decimation Linear scaling with length: method of N order Building block 1 Right lead Building block 1 Building block 2 Pristine block Building block 3 Left lead

29. Semi-infinite systems

30. → Finite size Hamiltonian Channel Left lead Right lead ~ HL 0 VLC ~ VCL HC VCR H = ~ VRC HR 0 NLorb NCorb NRorb Finite system

31. 0 ~ VLC GLC E-HL ~ VCL VCR GCL GC GCR E-HC VRC GRC ~ 0 E-HR 1 0 0 0 1 0 1 0 0 Green´s function technique System Green´s function: where: · = ~ (1) GCL (E-HL) +GC VCL = 0 ~ (2) GCL VLC +GC (E-HC) + GCRVRC = 1 ~ (3) GC VCR +GCR (E-HR) = 0

32. Left & Right lead self-energies ~ HC ΣL ΣR Green´s function technique System Green´s function: ~ GCL GCL = -GC VCL gL (E-HL) +GC VCL = 0 (1) ~ ~ GC = [ E-HC - ΣL- ΣR ] - 1 GCL VLC +GC (E-HC) + GCRVRC = 1 (2) ~ GCR = -GC VCR gR GC VCR +GCR (E-HR) = 0 (3) where: gL= [ E- HL ]-1 gC = [ E- HC]-1

33. Results FunctionalizedCNTs

34. Quasi-ballistic Diffusive Localized Transport regimes

35. Metallic CNTs Diffusive regime phenyls in 300 nm 200 configurations

36. Metallic CNTs Quasi-ballistic regime Carbenes in 1000 nm 200 configurations

37. Semiconducting CNTs →Small radius: quasi-ballistic →Large radius: diffusive !!! 1000 nm

38. Semiconducting CNTs Parallel orientation CH2 →sp3 signature in “metallic” tubes →CH2 vs 2H 2 Hydrogens

39. Results FunctionalizedGNRs

40. OH/H vs phenyls → sp3rehybridization signature → T(E) is independent of functional group 2 nm wide 4 nm wide

41. OH/H functionalization → Backscatteringsupression foredgefunctionalization → Conductancedips → Quantum mechanicalinterferences A. L. Bezanilla, F. Triozon, S.Roche Nano Letters 9, 2737 (2009)

42. Long nanoribbons (large gap) 4 nm wide Mean free path A. L. Bezanilla, F. Triozon, S.Roche Nano Letters 9, 2737 (2009)

43. Long nanoribbons (small gap) 4 nm wide Mean free path A. L. Bezanilla, F. Triozon, S.Roche Nano Letters 9, 2737 (2009)

44. Results Edgedefects in GNRs

45. Edge defects Experimental evidences → Z. Liu, K. Suenaga, P.J.F. Harris, S. Iijima, Phys. Rev. Lett. 102, 015501 (2009) →P. Koskinen, S. Malola, H. Hakkinen, Phys. Rev. Lett. 101, 115502 (2008).

46. Benzenoid defects S.Dubois, A. L.-Bezanilla et al. Submitted to PRL

47. Doping defects Passivated Acceptor sp3-like Donor Radical passivation Backscattering suppression

48. Conclusions Decimation technique → Full ab initio transport studies: SIESTA +TB_Sim Carbon Nanotubes → Chemical modification leads to diffusive transport → sp2 vs sp3 functionalization Graphene Nanoribbons → sp3 defects induce backscattering → Mind the radicals!  → Benzenoid edge defects are not critical in electronic transport properties

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