Synergistic Regulation of Superconductivity by Electron Localization and Phonon Frequency partition in Endohedral Carbon Cage Compounds XC₂₀

In this work, we employ first-principles calculations and take the C₂₀ carbon cage covalent framework as the research system to systematically investigate the modulation effect of different endohedral atoms X on the electron-phonon coupling (EPC) strength and superconducting transition temperature T_C of XC₂₀ compounds. We focus on elucidating the microscopic physical mechanism for the remarkable differences in superconducting properties within the identical carbon cage skeleton. Our results demonstrate that endohedral atoms exert synergistic modulation from two dimensions: electronic structure and phonon spectrum. On the electronic side, the charge transfer effect simultaneously modulates both the density of states at the Fermi level N(E_F) and the degree of spatial localization of Fermi-level electrons, which determines the electronic baseline strength of EPC. On the phonon side, the characteristic vibrational frequency of endohedral atoms is jointly determined by atomic mass and binding strength, and low-frequency localized vibrational modes can participate in the EPC process more efficiently. The degree of synergistic matching between the two sides ultimately determines the T_C of the systems. Among them, ClC₂₀ and PC₂₀ achieve the highest T_C values of 29.6 K and 19.8 K, respectively. This work reveals the superconductivity modulation rule of endohedrally doped carbon cage systems, and provides theoretical support for the design of ambient-pressure carbon-based superconducting materials.