Superconductivity in Carbon Cage-Like Substance C ₆ X (X = B, Na) under Pressure

Since the discovery of superconductivity, increasing the critical temperature ( T C ) has always been a core challenge. This study is based on the “element substitution” strategy, proposing to construct new C 6 X systems by replacing atoms in the CaH 6 cage-like structure. The study systematically explores the multidimensional coupling mechanism of “structure - electron - phonon” in these systems. The research focuses on the stability, electron–phonon coupling, and superconducting properties of the C 6 X (X = B, Na) systems, and reaches the following conclusions. The C 6 B system can maintain dynamic stability at normal pressure, but its dominant low-frequency phonon mode limits the superconducting transition temperature (29.13 K). Second, C 6 Na exhibits structural stability at 20 GPa and demonstrates enhanced electron–phonon coupling (EPC) strength (λ = 3.29), attributable to its pronounced charge transfer capability, high-frequency phonon modes, and highly symmetric, degeneracy-protected density of states (DOS), collectively elevating the superconducting critical temperature ( T C ) to 85.94 K. Finally, applying pressure leads to a decrease in the T C of the C 6 X system. Additionally, the study further proposes design principles for enhancing the T C of the C 6 X system. By enhancing the Fermi surface DOS through high charge transfer, inducing degenerate states near the Fermi energy ( E F ) with high symmetry, and leveraging multichannel electron–phonon coupling to break through the traditional coupling strength limitations. This work provides a theoretical basis for understanding the element regulation mechanism of carbon-based cage superconductors and optimizing superconducting properties, and points out the direction for the design of carbon-based superconducting materials at ambient pressure.