Superconducting and charge-density wave instabilities in ultrasmall-radius carbon nanotubes

TL;DR

This study investigates the electronic, phononic, and interaction properties of ultrasmall-radius carbon nanotubes, revealing competing superconducting and charge-density wave phases influenced by Coulomb interactions and nanotube size.

Contribution

It provides a detailed analysis of electron-phonon interactions and phase instabilities in small-radius CNTs, highlighting the dominance of charge-density waves or superconductivity depending on nanotube size and Coulomb effects.

Findings

(5,0) CNTs favor charge-density wave order without Coulomb interactions.

Including Coulomb interactions suppresses CDW and promotes superconductivity in (5,0) CNTs.

(6,0) CNTs exhibit dominant charge-density wave order with a transition temperature around 5 K.

Abstract

We perform a detailed analysis of the band structure, phonon dispersion, and electron-phonon coupling of three types of small-radius carbon nanotubes (CNTs): (5,0), (6,0), and (5,5) with diameters 3.9, 4.7, and 6.8 \AA respectively. The large curvature of the (5,0) CNTs makes them metallic with a large density of states at the Fermi energy. The density of states is also strongly enhanced for the (6,0) CNTs compared to the results obtained from the zone-folding method. For the (5,5) CNTs the electron-phonon interaction is dominated by the in-plane optical phonons, while for the ultrasmall (5,0) and (6,0) CNTs the main coupling is to the out-of-plane optical phonon modes. We calculate electron-phonon interaction strengths for all three types of CNTs and analyze possible instabilities toward superconducting and charge-density wave phases. For the smallest (5,0) nanotube, in the mean-field approximation and neglecting Coulomb interactions, we find that the charge-density wave transition temperature greatly exceeds the superconducting one. When we include a realistic model of the Coulomb interaction we find that the charge-density wave is suppressed to very low temperatures, making superconductivity dominant with the mean-field transition temperature around one K. For the (6,0) nanotube the charge-density wave dominates even with the inclusion of Coulomb interactions and we find the mean-field transition temperature to be around five Kelvin. We find that the larger radius (5,5) nanotube is stable against superconducting and charge-density wave orders at all realistic temperatures.