Effect of Electron-Phonon Interactions against Electron-Electron Interactions in Carbon Nanotubes

Abstract

We have studied the effect of electron-phonon interactions against electron-electron interactions in carbon nanotubes. For this purpose we have used renormalization group method combined with a two cut off scaling scheme. This method allowed for low temperature phases without bias. We have studied on metallic single wall nanotubes with short range interactions and their wrapping were armchair or zigzag.  We have studied the influence of electron-phonon coupling on low temperature phases of metallic single wall carbon nanotubes. In armchair carbon nanotube we have found that the phases induced by short range electronic correlations turned into a Peierls insulator by electron-phonon coupling. We have presented that the intraband scattering modes caused the softening and the radial breathing mode or the transverse optical mode was soften. In the case of zigzag carbon nanotubes no Peierls instability was found. This indicated that D-Mott phase or charge density wave appeared in zigzag carbon nanotubes. The effect of electron-phonon coupliong in zigzag carbon nanotubes do not produce a phonon softening instability and coupling is significant in this case. The phase diagrams of metallic armchair and zigzag carbon nanotubes are similar in the absence of electron-phonon coupling. We have also studied the behaviors of nanotubes based on renormalization equations became simple for carbon nanotubes. The obtained results were found in good agreement with previous obtained results.