Title: Interpretation of the Raman spectra of graphene and carbon nanotubes: the effects of Kohn anomalies and non-adiabatic effects
1Interpretation 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
2G-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
3Common interpretation curvature
Jorio et al. PRB 65, 155412 (2002)
G no diameter dependence ? LO axial
G- diameter dependence ? TO circumferential
4Common 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
5Kohn 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
6Kohn anomalies when?
Everything depends on the geometry of the Fermi
surface
q phonon wavevector k electron wavevector
- k1 k2 k1q 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
7Kohn 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
8Kohn 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
9Kohn anomalies in nanotubes
Metallic tubes same geometrical conditions as
graphite
- Metallic tubes two Giant Kohn anomalies predicted
- Semi-conducting tubes NO Kohn anomalies predicted
10Metallic tubes LO-TO splitting
- TO
- Circumferential
- No KA
- ? G
Opposite Interpretation
10
11Dynamic 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
12Dynamic effects in nanotubes
- KA_at_LO smeared
- New KA_at_TO
- LO increased
- TO decreased
13Dynamic 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
14LO and TO frequencies
15Th Vs Exp Room Temperature
- Metallic tubes
- G-?LO G?TO
- Semiconducting tubes
- G- ?TO G ?LO
- Fermi golden rule
- EPC? FWHM(G-)
-
16Interpretation 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)
17G- 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)
18G- 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
20Conclusions
- 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 -