Theory of size-dependent resonance Raman scattering from carbon nanotubes

Raman scattering from single-walled carbon nanotubes is examined in detail theoretically and compared with experiments. Within a simple tight-binding model the Raman matrix elements are evaluated explicitly, and the shape of the resonance in the scattered intensity due to interband electronic transitions is derived. The resonance in the optical regime is shown to depend sharply on the diameter of the tubes. Thus, resonance Raman scattering may be used for determining size distribution in a sample, as well as for the determination of details of the band structure.