This work reports how resonance Raman experiments are used to study details of the electronic structure of individual single-wall carbon nanotubes (SWNTs) by measuring the phonon ·spectra and how the quantized electronic structure affects the dispersive Raman features of SWNTs. We focus our analysis on the dispersive D and G′ bands observed in the Raman spectra of isolated semiconducting nanotubes. By using a laser excitation energy of 2.41 eV, we show that both the D-band and G′-band frequencies are dependent on the wave vector kii where the electrons are confined in the one-dimensional subband i of the electronic structure of SWNTs. By making use of the (n,m) assignment for each tube, we theoretically correlate the observed frequency dependences for the D- and G′-band modes with the electronic structure predicted for each (n,m) pair and we determine the dependence of ωD and ωG′ on the diameter and chirality for individual electronic transitions Eii for nanotube bundles. We use the D- and G′-band dependence on electron wave vector kii to predict the dominant phonon wave vector q selected by the quantum-confined electronic state kii and to explain the anomalous dispersion observed for ωD and ωG′ in SWNT bundles as a function of laser excitation energy, yielding excellent agreement between experiment and theory.
|Original language||English (US)|
|Number of pages||6|
|Journal||Physical Review B - Condensed Matter and Materials Physics|
|State||Published - Jan 15 2002|
ASJC Scopus subject areas
- Electronic, Optical and Magnetic Materials
- Condensed Matter Physics