Fig. 1. Phase stability and crystal structures of Li–C–P ternary compounds. (a) Ternary enthalpy phase diagram of Li–C–P system at 300 GPa. Gray squares represent metastable or unstable phases (above the convex hull) with different E_hull. The stars within the triangle represent thermally stable phases (located on the convex hull), while pink stars positioned on the vertices and edges of the triangle represent the corresponding stable elements and binary compounds. (b) Crystal structure of R3-Li₁₄CP with rhombohedral primitive cell at 300 GPa. The excess electrons (yellow spheres) are located at the body-center position of the double hexagonal pyramid (NNA1) and dodecahedron (NNA2). The isosurface value is 0.75. Pink, blue, and brown spheres represent Li, P, and C atoms, respectively.

Fig. 2. Electronic structure of Li₁₄CP at 300 GPa. (a) Band structure. The Fermi level E_F is defined as the origin (dashed line), and the three bold dispersion curves represent the bands across E_F, primarily composed of electronic states located around Li and NNAs. (b) Projected density of states (PDOS) on the spheres located at Li, C, P, and NNA positions. (c) Two-dimension ELF (top left) and band-decomposed electron density maps of the three bands crossing E_F on the (11̄0) plane (top right, bottom left, and bottom right), bisecting the rhombohedral primitive cell. The conduction electrons occupying electronic states within band I are distributed around NNA1 and diffuse toward adjacent Li atoms to form satellite interstitial electrons (SIEs).

Fig. 3. Electron–phonon coupling and mechanism of superconductivity in Li₁₄CP. (a) Pressure-modulated electron density maps of band I crossing E_F on the (11̄0) plane, in which the electron densities of the SIEs increase with increasing pressure. (b) Pressure-modulated EPC parameter λ, superconducting critical temperature T_c, number of electrons at the centers of SIEs N_SIEs, and negative integrated COHP (−ICOHP) of the NNA1–Li5 pair. (c) Phonon dispersion curve with q-resolved EPC parameter λ_q at 300 GPa, where the radii of the brown circles are proportional to the strength of λ_q. (d) Eliashberg spectral function α²F(ω) and integral EPC parameter λ as a function of frequency. (e) Fermi surface nesting function ξ(q) along special q trajectories.

Fig. 4. Hole-doping-modulated electronic properties and superconductivity at 300 GPa. (a) EPC parameter λ, superconducting critical temperature T_c, and percentage contributions to λ of low-frequency acoustic branches below 8 THz. (b) Low-frequency acoustic branches with the q-resolved EPC parameter λ_q; the doping concentrations from top to bottom are 1, 0.4, and 0e, respectively. (c) Fermi surface nesting function ξ(q) along special q trajectories. (d) Sign of the Laplacian of the electron density [∇²ρ(r)] between NNA1 and Li5; the small black sphere in the inset corresponds to the bond critical point (BCP).

Fig. 5. Mechanisms of superconductivity in Li₆P and Li₆C. (a) Two-dimensional ELF. There are connected dumbbell-like and cage-state NNAs in Li₆P and Li₆C. (b) Electron density maps of the bands crossing E_F, in which there are obvious SIEs between NNAs and the adjacent Li atoms. (c) Pressure-modulated superconducting critical temperature T_c and electron density of SIEs N_SIEs.