Superconductivity in compounds of sodium-intercalated graphite

The discovery of superconductivity in $\mathrm{Ca}{\mathrm{C}}_{6}$ with a critical temperature (${T}_{c}$) of 11.5 K reignited much interest in exploring high-temperature superconductivity in graphite intercalation compounds (GICs). Here we identify a GIC $\mathrm{Na}{\mathrm{C}}_{4}$, discovered by ab initio evolutionary structure search, as a superconductor with a computed ${T}_{c}$ of 41.2 K at 5 GPa. This value is eight times higher than that of the synthesized GIC $\mathrm{Na}{\mathrm{C}}_{2}$ and possesses the highest ${T}_{c}$ among available GICs. The remarkable superconductivity of GIC $\mathrm{Na}{\mathrm{C}}_{4}$ mainly arises from the coupling of \ensuremath{\pi} electrons in graphene with the low-frequency vibrations involving both Na and C atoms. These findings suggest that Na GICs may hold great promise as high-${T}_{c}$ superconductors.