T-carbon has been proposed as a new carbon allotrope in 2011, which was successfully synthesized in recent experiments. Because of its fluffy structure, several kinds of atoms can be intercalated into T-carbon, making it a versatile candidate in various applications such as hydrogen storage, perovskite solar cells, lithium ion batteries, thermoelectrics, photocatalyst, etc. Here we show that superconductivity can appear in Na-doped T-carbon with superconducting transition temperature Tc of 11 K at ambient pressure, and Tc can be enhanced to 19 K under pressure of 14 GPa, which results from an enhancement of the electron-phonon coupling due to the shift of the phonon spectral weight to lower frequencies with the increase of pressure. The calculations on specific heat and electrical and thermal conductivities show that the normal state of the Na-doped T-carbon superconductor reveals a non-Fermi liquid behavior. The prediction of superconductivity in Na-doped T-carbon would spur great interest both experimentally and theoretically to explore novel carbon-based superconductors.
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