Analytical approach to phonons and electron-phonon interactions in single-walled armchair carbon nanotubes

Phonon spectra are calculated in single-walled armchair carbon nanotubes within a mass and spring model. Classical Hamiltonian for the lattice vibrations that include nearest-neighbor, next-nearest-neighbor, and bond bending interactions has been quantized in the usual way, and then the phonon Hamiltonian is diagonalized by canonical transformations. Resolvent formalism is used to obtain phonon frequencies in analytical forms, where a procedure of the Fano problem is employed to choose correct phonon modes. The force constants are chosen from previous works, and the Raman mode at 1600 cm(-1) is set to obtain the other modes. The electron-phonon interaction is investigated by phonon modulation of the hopping interaction, where the same canonical transformations are used in accordance with the phonon part. The electron-phonon coupling strengths in intraband and interband scattering for all modes within nearest-neighbor and radial bond bending interactions are found in terms of the q wave vectors and other parameters. Further, a different approach for the diagonalization of the electronic part arising from the tight-binding Hamiltonian is also presented in accordance with the electron-phonon interaction part.