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

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 $\lambda$ 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.