Electron-phonon effects in graphene and armchair (10,10) single-wall carbon nanotubes

The electron-phonon interaction in low-dimensional tight-binding systems is discussed. A sheet of graphite, which is two-dimensional, and an armchair single-wall carbon nanotube (SWNT), which is quasi-one-dimensional, are tak en as examples. For the modulated hopping the matrix elements for both syst ems are derived in the context of a two parameter model. for the phonon vib rational spectrum. It is found that they (for both structures) display a de formation type of potential, and are reduced by a factor of (I-R), where R depends on the phonon parameters. It is also shown that the ordinary electr on-phonon coupling displays a deformation type of approximation for both sy stems. Next, a different type of interaction is considered-the phonon modul ated electron-electron interaction. It gives two contributions-random phase approximation with one phonon Line and exchange interaction with one phono n line. We find that for the two-dimensional (2D) graphene and for the quas i-ID (10,10) SWNT, the modulated hopping and exchange coupling govern the e lectron transport at room temperatures.