Electron-phonon matrix elements in single-wall carbon nanotubes

Abstract

We have developed the electron-phonon matrix element in single-wall carbon nanotubes by using the extended tight-binding model based on density functional theory. We calculate this matrix element to study the electron-phonon coupling for the radial breathing mode (RBM) and the $G$-band $A$ symmetry modes of single-wall carbon nanotubes. Three well-defined family patterns are found in the RBM, longitudinal optical (LO) mode and transverse optical (TO) mode. We find that among the RBM, LO, and TO modes, the LO mode has the largest electron-phonon interaction. To study the electron-phonon coupling in the transport properties of metallic nanotubes, we calculate the relaxation time and mean free path in armchair tubes. We find that the LO mode, ${A}_{1}^{\ensuremath{'}}$ mode, and one of the ${E}_{1}^{\ensuremath{'}}$ modes give rise to the dominant contributions to the electron inelastic backscattering by phonons. Especially, the off-site deformation potential gives zero matrix elements for ${E}_{1}^{\ensuremath{'}}$ modes while the on-site deformation potential gives rise to nonzero matrix elements for the two ${E}_{1}^{\ensuremath{'}}$ modes, indicating that the on-site deformation potential plays an important role in explaining the experimentally observed Raman mode around $2450\phantom{\rule{0.3em}{0ex}}{\mathrm{cm}}^{\ensuremath{-}1}$ in carbon.