Probing phonon dispersion relations of graphite by double resonance Raman scattering.

Double-resonant Raman scattering in graphite: Interference effects, selection rules, and phonon dispersion

We present a comprehensive analysis of double-resonant Raman scattering in graphite and derive an analytical expression for the Raman cross section of the D mode in one dimension. The extension to two dimensions does not change the double-resonant phonon wave vectors. In the full integration of the Raman cross section, the contributions by phonons from exactly the K point cancel due to destruct...

Origin of the unusual dependence of Raman D band on excitation wavelength in graphite-like materials

We have revisited the still unresolved puzzle of the dispersion of the Raman disorder-induced D band as a function of laser excitation photon energy EL in graphite-like materials. We propose that the D mode is a combination of an optic phonon at the K point in the Brillioun zone and an acoustic phonon whose momentum is determined uniquely by the double resonance condition. The fit of the experi...

Raman spectroscopy of graphite.

We present a review of the Raman spectra of graphite from an experimental and theoretical point of view. The disorder-induced Raman bands in this material have been a puzzling Raman problem for almost 30 years. Double-resonant Raman scattering explains their origin as well as the excitation-energy dependence, the overtone spectrum and the difference between Stokes and anti-Stokes scattering. We...

Determination of two-dimensional phonon dispersion relation of graphite by Raman spectroscopy

Raman intensity of single-wall carbon nanotubes

Using nonresonant bond-polarization theory, the Raman intensity of a single-wall carbon nanotube is calculated as a function of the polarization of light and the chirality of the carbon nanotube. The force-constant tensor for calculating phonon dispersion relations in the nanotubes is scaled from those for two-dimensional graphite. The calculated Raman spectra do not depend much on the chiralit...