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 one single sharp G peak corresponding to q==0, mode E2g Nanotubes: Two main bands, G+ and G-. Modes derived from graphite E2g Metallic  semiconducting Calculation of D_q for graphene: trivial and cheap. Restricting

Common interpretation: curvature Jorio et al. PRB 65, 155412 (2002) G+: no diameter dependence  LO axial Calculation of D_q for graphene: trivial and cheap. Restricting G- diameter dependence  TO circumferential

Common interpretation: Fano resonance In metallic tubes the G- peak is: Downshifted Broader Depends on diameter Interpretation Fano resonance Phonon-Plasmon interaction Calculation of D_q for graphene: trivial and cheap. Restricting Electron-phonon coupling and Kohn anomalies have to be considered

Kohn anomalies Atomic vibrations are screened by electrons In a metal 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 Calculation of D_q for graphene: trivial and cheap. Restricting

Kohn anomalies: when? Everything depends on the geometry of the Fermi surface k1 k2 = k1+ q q Fermi surface q = phonon wavevector k = electron wavevector Calculation of D_q for graphene: trivial and cheap. Restricting k1 & k2= k1+q on the Fermi surface Tangents to the Fermi surface at k1 and k2= k1+ q are parallel W. Kohn, Phys. Rev. Lett. 2, 393 (1959) bold

Kohn anomalies in graphite Graphite is a semi metal: Fermi surface = 2 points: K and K’ = 2 K K K’ p* E G q = K-K = 0 = G G G q = K’-K = 2K - K = K K G EF G p Calculation of D_q for graphene: trivial and cheap. Restricting Kohn Anomalies for:

Kohn anomalies in graphite IXS data: J. Maultzsch et al. Phys. Rev. Lett. 92, 075501 (2004) E2g A’1 E2g Calculation of D_q for graphene: trivial and cheap. Restricting 2 sharp kinks for modes E2g at G and A1’ at K Kohn Anomaly EPC ≠ 0

Kohn anomalies in nanotubes Metallic tubes: same geometrical conditions as graphite Ef p* p Calculation of D_q for graphene: trivial and cheap. Restricting Metallic tubes: two Giant Kohn anomalies predicted Semi-conducting tubes: NO Kohn anomalies predicted

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

Rely on Born-Oppenheimer approximation: electrons see fixed ions 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 Calculation of D_q for graphene: trivial and cheap. Restricting This is no longer true for 1D systems The dynamic nature of phonons can be taken into account Beyond Born-Oppenheimer…

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

Phonons are not static deformations 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

LO and TO frequencies

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

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)

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 Calculation of D_q for graphene: trivial and cheap. Restricting Krupke et al. Science 301, 344 (2003)

G- band Vs T: experiments Calculation of D_q for graphene: trivial and cheap. Restricting Semiconducting tubes: G+ - G- constant  Anharmonicity Metallic tubes: G+ - G- increases with T  ??? (EPC)

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

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