Fig. 1. (a) Convex hull constructed with thermodynamically stable P–S compounds at 50 and 100 GPa. For clarity, we have offset the formation enthalpy by −0.1 eV for 100 GPa. The full convex hull is shown in Fig. S1. (b) Pressure–composition phase diagram of stable P–S compounds.

Fig. 2. Crystal structures of (a) Cmcm P₅S at 100 GPa, (b) P-31m P₈S at 100 GPa, (c) P-1 P₁₁S at 50 GPa, (d) P-3m1-I PS₂ at 50 GPa, (e) C2/m PS₂ at 100 GPa, and (d) P-3m1-II PS₂ at 200 GPa. Blue and yellow spheres represent P and S atoms, respectively.

Fig. 3. (a) Schematic diagram of the bonding mechanism in sc P. (b) Average bonding unsaturation, (c) T_c and EPC parameters λ, and the logarithmic average phonon frequency ω_log values, (d) total DOS NEF per atom, and PDOS of P atom NEF(P) at E_F, (e) lengths of P–P and P–S bonds, and the highest phonon frequency of five P-rich P–S compounds (P₂S, P₃S, P₅S, P₈S, and P₁₁S). (f) T_c and calculated average bonding unsaturation values of H₂₉ cage assuming that all valence electrons of the transition metal (TM) are transferred to the H cages in well-known superconducting TM hydrides (P6₃/mmc TMH₉, TM = Y, Th, and Pr) at 120–150 GPa.

Fig. 4. (a) ELF, (b) PDOS, (c) projected electronic band structure, (d) PHDOS and Eliashberg spectral function and λ(ω), (e) phonon dispersion curves (the magnitude of λ is indicated by the thicknesses of the red curves), and (f) pressure-dependent T_c, λ, and ω_log of P-31m P₈S.