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Interpretation of the Raman spectra of graphene and carbon nanotubes: the effects of Kohn anomalies and non-adiabatic ef

Interpretation of the Raman spectra of graphene and carbon nanotubes: the effects of Kohn anomalies and non-adiabatic effects. S. Piscanec Cambridge University Engineering Department: Centre for Advanced Photonics and Electronics, Cambridge, UK. G-band in graphite and nanotubes. Graphite :

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Interpretation of the Raman spectra of graphene and carbon nanotubes: the effects of Kohn anomalies and non-adiabatic ef

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  1. Interpretation of the Raman spectra of graphene and carbon nanotubes: the effects of Kohn anomalies and non-adiabatic effects S. Piscanec Cambridge University Engineering Department: Centre for Advanced Photonics and Electronics, Cambridge, UK

  2. G-band in graphite and nanotubes Graphite: one single sharp G peak corresponding to q==0, mode E2g • Nanotubes: • Two main bands, G+ and G-. • Modesderived from graphite E2g • Metallic  semiconducting

  3. Common interpretation: curvature Jorio et al. PRB 65, 155412 (2002) G+: no diameter dependence  LO axial G-diameter dependence TO circumferential

  4. Common interpretation: Fano resonance • In metallic tubes the G- peak is: • Downshifted • Broader • Depends on diameter • Interpretation • Fano resonance • Phonon-Plasmon interaction Electron-phonon coupling and Kohn anomalies have to be considered

  5. Kohn anomalies • Atomic vibrations are screened by electrons • In ametal this screening abruptly changes for vibrations associated to certain q points of the Brillouin zone. • Kink in the phonon dispersions: Kohn anomaly. • Graphite is a semi-metal • Nanotubes are folded graphite • Nanotubes can as well be metallic

  6. Fermisurface k2 = k1+ q q k1 Kohn anomalies: when? Everything depends on the geometry of the Fermi surface q= phonon wavevector k = electron wavevector • k1 & k2= k1+q on the Fermi surface • Tangents to the Fermi surface at k1and k2= k1+ q are parallel • W. Kohn, Phys. Rev. Lett. 2, 393 (1959) bold

  7. G G K • q =K-K= 0 = G • q =K’-K = 2K - K = K Kohn anomalies in graphite • Graphite is a semi metal: • Fermi surface = 2 points: K and K’ = 2 K K K’ p* E G G G EF G p Kohn Anomalies for:

  8. Kohn anomalies in graphite IXS data: J. Maultzsch et al. Phys. Rev. Lett. 92, 075501 (2004) E2g A’1 E2g • 2 sharp kinks formodesE2g at G and A1’ at K Kohn Anomaly EPC ≠ 0

  9. p* Ef p Kohn anomalies in nanotubes Metallic tubes: same geometrical conditions as graphite • Metallic tubes: two Giant Kohn anomalies predicted • Semi-conducting tubes: NO Kohn anomalies predicted

  10. Metallic tubes: LO-TO splitting • TO: • Circumferential • No KA •  G+ • LO: • Axial • strong EPC •  G- Opposite Interpretation 10

  11. Dynamic Effects • Frozen phonons • Finite differences • Density functional perturbation theory Rely on Born-Oppenheimer approximation: electrons see fixed ions Static approaches For 3D crystals this is 100% OK This is no longer true for 1D systems • The dynamic nature of phonons can be taken into account • Beyond Born-Oppenheimer…

  12. Dynamic effects in nanotubes • KA@LO: smeared • New KA@TO • LO: increased • TO: decreased

  13. Dynamic effects Phonons are not static deformations • T increases: • KA@LO: weaker • KA@TO: no changes • d increases: • KA@LO: weaker • KA@TO: weaker • KA@LO: smeared • New KA@TO

  14. LO and TO frequencies

  15. Th Vs Exp: Room Temperature • Metallic tubes: • G-LO & G+TO • Semiconducting tubes: • G- TO & G+ LO • Fermi golden rule: • EPC FWHM(G-)

  16. Interpretation of Raman spectra TO – circumferential LO – axial • Semiconducting: • LO-TO splitting  curvature • G+ axial • G-  circumferential LO – axial TO – circumferential • Metallic: • LO-TO splitting  Kohn an. • G+ circumferential • G-  axial (KA) • FWHM(G-)  EPC • G- interpretation: EPC and not • Phonon-plasmon resonance Piscanec et al. PRB (2007)

  17. G- band Vs T: experiments • Metallic SWNTs • Dielectrophoresis • HiPCo SWNTs (Houston), d~1.1nm • Vpp = 20 V and f=3MHz • Raman Spectroscopy •  = 514 nm (resonant with semicon.) •  = 633 nm (resonant with metallic) • Linkam stage: 80K < T < 630K Krupke et al. Science 301, 344 (2003)

  18. G- band Vs T: experiments • Semiconducting tubes: G+ - G- constant  Anharmonicity • Metallic tubes: G+ - G- increases with T  ??? (EPC)

  19. Th Vs Exp: Temperature Dependence Metallic tubes from R. Krupke

  20. Conclusions • Measurement of the Raman G-band Vs T • Metallic tubes from dielecrophoresis • Semiconducting tubes  G+ - G- = constant • Metallic tubes  G+ - G- changes with T • Kohn anomalies and electron phonon coupling and dynamic effects • Interpretation of G-band in SWNTs Raman spectra • Explanation of the T-dependence of the G- in metallic SWNTs

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