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

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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
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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-.
• Modes derived from graphite E2g
• Metallic ? semiconducting

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

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Kohn anomalies when?
Everything depends on the geometry of the Fermi
surface
q phonon wavevector k electron wavevector

1. k1 k2 k1q on the Fermi surface
2. Tangents to the Fermi surface at k1 and k2 k1
   q are parallel

• W. Kohn, Phys. Rev. Lett. 2, 393 (1959) bold

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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
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Kohn anomalies in graphite
IXS data J. Maultzsch et al. Phys. Rev. Lett.
92, 075501 (2004)
E2g
A1
E2g

• 2 sharp kinks for modes E2g at G and A1 at K

Kohn Anomaly
EPC ? 0
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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

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Metallic tubes LO-TO splitting

• TO
• Circumferential
• No KA
• ? G

• LO
• Axial
• strong EPC
• ? G-

Opposite Interpretation
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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

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Dynamic effects in nanotubes

• KA_at_LO smeared
• New KA_at_TO

• LO increased
• TO decreased

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Dynamic effects
Phonons are not static deformations

• T increases
• KA_at_LO weaker
• KA_at_TO no changes

• d increases
• KA_at_LO weaker
• KA_at_TO weaker

• KA_at_LO smeared
• New KA_at_TO

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LO and TO frequencies
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Th Vs Exp Room Temperature

• Metallic tubes
• G-?LO G?TO
• Semiconducting tubes
• G- ?TO G ?LO
• Fermi golden rule
• EPC? FWHM(G-)

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Interpretation of Raman spectra
TO circumferential
LO axial

• Semiconducting
• LO-TO splitting ? curvature
• G ? axial
• G- ? circumferential

TO circumferential
LO axial

• 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)
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G- band Vs T experiments

• Metallic SWNTs
• Dielectrophoresis
• HiPCo SWNTs (Houston), d1.1nm
• Vpp 20 V and f3MHz
• Raman Spectroscopy
• ? 514 nm (resonant with semicon.)
• ? 633 nm (resonant with metallic)
• Linkam stage 80K lt T lt 630K

Krupke et al. Science 301, 344 (2003)
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G- band Vs T experiments

• Semiconducting tubes G - G- constant ?
  Anharmonicity
• Metallic tubes G - G- increases with T ? ???
  (EPC)

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Th Vs Exp Temperature Dependence
Metallic tubes from R. Krupke
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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