Superconductivity in sodium-doped T-carbon

T-carbon had 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 potential versatile candidate in various applications such as hydrogen storage, solar cells, lithium ion batteries, thermoelectrics, photocatalyst, etc. Here we show that superconductivity can appear in Na-doped T-carbon with a superconducting transition temperature $T_c$ of 11 K at ambient pressure, and $T_c$ can be enhanced to 19 K under a pressure of 14 GPa. The calculations on temperature dependence of specific heat and electrical and thermal conductivities show that the normal state of the Na-doped T-carbon superconductor is a non-Fermi liquid at temperature below 50 K, where the Wiedemann-Franz law is remarkably violated. The prediction of superconductivity in Na-doped T-carbon would spur great interest both experimentally and theoretically to explore novel carbon-based superconductors.

Figure 1

(a) The cubic crystalline structure of Na-doped T-carbon ${\mathrm{NaC}}_8$ with Na atoms (green balls) occupying the Wyckoff position $4a$. (b) The Fermi surface of Na-doped T-carbon.

Figure 2

(a) The simulated x-ray diffraction (XRD) spectra, (b) infrared (IR) spectra, and (c) Raman spectra of Na-doped T-carbon. The x ray with wavelength of 1.54 Å is used.

Figure 3

(a) The electron band structure and (b) the partial density of states of the Na-doped T-carbon with inclusion of the SOC. The left lower inset in (a) is the enlarged part marked by the red dashed cycle in band structures.

Figure 4

(a) The phonon spectra and (b) the phonon density of states (PhDOS) (divided by 40), Eliashberg spectral function ${\alpha }^{2}F\left(\omega \right)$, and the cumulative frequency-dependent of EPC $\lambda \left(\omega \right)$ of Na-doped T-carbon at ambient pressure.

Figure 5

(a) Temperature dependence of electronic specific heat $C$ in the normal state of Na-doped T-carbon superconductor. The upper and lower insets are the enlarged parts of the specific heat at temperature $T<15\mathrm{K}$ and $15<T<50\mathrm{K}$, respectively. The dash lines are fitting curves at different temperature regions. (b) Temperature dependent Lorenz number $L$ $[L=\kappa /(\sigma T\left)\right]$. The inset exhibits the temperature dependent electrical ($\sigma$) and thermal ($\kappa$) conductivities over the relaxation time ($\tau$).

Figure 6

Pressure dependence of (a) logarithmic superconducting transition temperature, (b) Hopfield ($d\ln \eta /d\ln V$), and Grüneisen ($\gamma$) parameters in Eq. (7) for the Na-doped T-carbon superconductor.

Figure 7

The Eliashberg spectral functions ${\alpha }^{2}F\left(\omega \right)$ under various pressure.