Electron-phonon interaction in ultrasmall-radius carbon nanotubes

Abstract

We perform analysis of the band structure, phonon dispersion, and electron-phonon interactions in three types of small-radius carbon nanotubes. We find that the s5,5d nanotube can be described well by the zonefolding method and the electron-phonon interaction is too small to support either a charge-density wave or superconductivity at realistic temperatures. For ultrasmall s5,0d and s6,0d nanotubes we find that the large curvature makes these tubes metallic with a large density of states at the Fermi energy and leads to unusual electron-phonon interactions, with the dominant coupling coming from the out-of-plane phonon modes. By combining the frozen-phonon approximation with the random phase approximation analysis of the giant Kohn anomaly in one dimension we find parameters of the effective Fröhlich Hamiltonian for the conduction electrons. Neglecting Coulomb interactions, we find that the s5,5d carbon nanotube sCNTd remains stable to instabilities of the Fermi surface down to very low temperatures while for the s5,0d and s6,0d CNTs a charge density wave instability will occur. When we include a realistic model of Coulomb interaction we find that the charge-density wave remains dominant in the s6,0d CNT with TCDW around5Kwhile the charge-density wave instability is suppressed to very low temperatures in the s5,0d CNT, making superconductivity dominant with transition temperature around 1 K.