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 ͑5,5͒ 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 ͑5,0͒ and ͑6,0͒ 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 ͑5,5͒ carbon nanotube ͑CNT͒ remains stable to instabilities of the Fermi surface down to very low temperatures while for the ͑5,0͒ and ͑6,0͒ 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 ͑6,0͒ CNT with T CDW around 5 K while the charge-density wave instability is suppressed to very low temperatures in the ͑5,0͒ CNT, making superconductivity dominant with transition temperature around 1 K.

Coulomb screening and electronic instabilities of small-diameter (5,0) nanotubes

“…where k stands for the energy of the exchanged phonon with momentum k. The typical energy of the phonons in the optical branches ͑or in the acoustic branches at large momentum transfer͒ is of the order of ϳ0.1 eV, 29 and therefore comparable to the energy cutoff E c of the 1D electron system. This allows us to take the interaction arising from ͑18͒ as a source of attraction, in the energy range where the 1D model makes sense.…”

“…27 We may compare the results of our investigation with those obtained for the small-diameter zigzag nanotubes by means of ab initio simulations 28 and mean-fieldlike calculations. 29 In Ref. 29, a superconducting instability has been found to be dominant in the ͑5,0͒ nanotubes, at a scale of about 1 K. On the other hand, a CDW instability has been identified in the same geometry at room temperature in Ref.…”

“…29 In Ref. 29, a superconducting instability has been found to be dominant in the ͑5,0͒ nanotubes, at a scale of about 1 K. On the other hand, a CDW instability has been identified in the same geometry at room temperature in Ref.…”

“…29 Similarly, for backscattering processes within the nondegenerate subband, we find the effective coupling ͚ 2͑g 00…”

“…The electron-phonon couplings in the ͑5,0͒ nanotubes have been analyzed with great detail in Ref. 29. It has been shown there that the couplings with greater strength correspond to intraband processes, for which the momentum transfer is in the longitudinal direction.…”