Electron-phonon interaction in ultrasmall-radius carbon nanotubes

摘要: We perform analysis of the band structure, phonon dispersion, and electron-phonon interactions in three types small-radius carbon nanotubes. find that (5,5) nanotube can be described well by zone-folding method interaction is too small to support either a charge-density wave or superconductivity at realistic temperatures. For ultrasmall (5,0) (6,0) nanotubes we large curvature makes these tubes metallic with density states Fermi energy leads unusual interactions, dominant coupling coming from out-of-plane modes. By combining frozen-phonon approximation random phase giant Kohn anomaly one dimension parameters effective Fr\"ohlich Hamiltonian for conduction electrons. Neglecting Coulomb (CNT) remains stable instabilities surface down very low temperatures while CNTs charge instability will occur. When include model CNT ${T}_{\mathrm{CDW}}$ around 5 K suppressed CNT, making transition temperature 1 K.