Electron-phonon coupling of one-dimensional (3,0) carbon nanotube

Abstract

A very recent report claims that ambient-pressure high-temperature ($T_c$) superconductivity was found in boron-doped three-dimensional networks of carbon nanotubes (CNTs). Here, we systematically study the electron-phonon coupling (EPC) of one-dimensional (1D) (3,0) CNT under ambient pressure. Our results show that the EPC constant $λ$ of the undoped 1D (3,0) CNT is 0.70, and reduces to 0.44 after 1.3 holes/cell doping. Further calculations show that the undoped (3,0) CNT is a two-gap superconductor with a superconducting $T_c$ $\sim$ 33 K under ambient pressure. Additionally, we identify three characteristic phonon modes with strong EPC, establishing that the pristine (3,0) CNT is a high-$T_c$ superconducting unit, and further suggest that searching for those superconducting units with strong EPC phonon mode would be an effective way to discover high-$T_c$ phonon-mediated superconductors. Our study not only provide a crucial and timely theoretical reference for the recent report regarding superconducting CNTs, but also uncover that the pristine (3,0) CNT hosts the highest record of superconducting $T_c$ among the elemental superconductors under ambient pressure.

Figures (5)

• Figure 1: Crystal structures for one-dimensional (a) (3,0) and (b) (2,1) carbon nanotubes, respectively.
• Figure 2: Electronic structures for (a-b) undoped and 1.3 holes/cell doped (3,0) and (c-d) undoped and 1.6 holes/cell doped (2,1) carbon nanotubes, respectively. The Fermi level is set to zero.
• Figure 3: Phonon spectrum with a color representation of $\lambda_{\bf{q}\nu}$, Eliashberg spectral function $\alpha^2F(\omega)$ and accumulated $\lambda(\omega)$ for (a-b) undoped and (c-d) 1.3 holes/cell doped (3,0) carbon nanotubes. The graduation of $\alpha^2F(\omega)$ is omitted for clarify. (e) Fermi-surface nesting function $\xi(\bf{q})$ of undoped and 1.3 holes/cell doped (3,0) carbon nanotubes. $\xi(\bf{q})$ is normalized by the corresponding value of $\xi(\Gamma)$.
• Figure 4: (a) and (b) Zoom-in pictures of phonon spectrums with $\lambda_{\bf{q}\nu}$ of undoped (3,0) carbon nanotube. Red arrows denote three different phonon modes with strong EPC. (c) Electron localization functions of undoped (3,0) carbon nanotube with vibration patterns of the $A_g$ and $B_{1g}$ phonon modes at the $\Gamma$ point. (d) The snapshots for the vibrations of the breathing mode that is near the $Z$ point of undoped (3,0) carbon nanotube.
• Figure 5: (a) Superconducting gap $\Delta$ of undoped (3,0) nanotube. The solid lines are fitting results. (b) and (c) Fermi points with EPC $\lambda$($\bf{k}$) of undoped (3,0) nanotube.