Exciton-phonon interaction and Raman intensity of carbon nanotubes*

Using extended tight binding framework, the exciton states and exciton-phonon interaction are calculated for understanding optical properties of single wall carbon nanotubes. Resonance Raman intensity for first and second order Raman processes are calculated as a function of $(n,m)$ with use of exciton wavefunctions. Chirality, type and diameter dependence of Raman intensity is now fully given. In particular, the dark exciton plays an important role for second-order, intervalley, resonance Raman processes. Although the exciton-phonon interaction is not so different from the electron-phonon interaction, the optical absorption (emission) is enhanced significantly by the localized exciton wavefunctions.\\ \ \\ References: J. Jiang et al, Phys. Rev. B, in press.