Stability-superconductivity map for compressed Na-intercalated graphite

We investigate the stability and superconductivity of compressed Na-intercalated graphite using advanced structure search and Migdal-Eliashberg methods. In addition to the previously proposed NaC₄ superconductor with a critical temperature (T_c) around 40 K in the 5-10 GPa range, we identify new synthesizable Na₃C₁₀, NaC₈, and NaC₁₂ compounds and map pressure-composition conditions defining high-T_c superconductivity driven by the nearly-free-electron-like intercalant states. We demonstrate that NaC₄ has a distinct two-gap structure unusual for electron-doped materials and that Na₃C₁₀ is an equally promising superconductor.