We report a study of the disorder-induced D band in the resonance Raman spectra of isolated single-wall carbon nanotubes (SWNTs). We show that the D-band frequency ωD depends directly on the nanotube diameter dt and also on the magnitude of the wave vector for the quantized states kii, where the van Hove singularities in the density of states occur. These two effects are manifested in the D-band frequency through the ωD=ωD0+Cld, functional form, but with C negative (positive) for the spring-constant- (doubleresonance-) dependent processes, thereby indicating that the spring constant softens and the double resonance stiffens the D-band frequencies. In the case of the spring constant effect, ωD0 is the frequency observed in two-dimensional graphite. The outcome of the softening versus stiffening competition depends on the nanotube diameter range. When plotted over a wide dt range, the diameter dependence of ωD (C<0) arises from the softening of the spring constants due to the nanotube curvature, but within a single interband transition Eii, whereby the dt variation is small, the D-band stiffening (C>0) due to the double-resonance condition becomes the dominant effect.
|Original language||English (US)|
|Number of pages||7|
|Journal||Physical Review B - Condensed Matter and Materials Physics|
|State||Published - Jan 15 2003|
ASJC Scopus subject areas
- Electronic, Optical and Magnetic Materials
- Condensed Matter Physics