Bonding-unsaturation-dependent superconductivity in P-rich sulfides

The covalent frameworks found in certain compounds,such as the S–H skeleton in H3S and the H cage in LaH10,play an essential role in their superconductivity.These compounds have the feature of bonding unsaturation(a deficiency of electrons in their covalent bonding)in common.Developing an understanding of the relationship between superconductivity and bonding unsaturation in these materials can provide new ideas for the design of superconducting materials.In this work,we explored the high-pressure phase diagram of binary P–S compounds using first-principles swarm structural calculations.In addition to the previously reported P2S and P3S structures,we identified that P5S,P8S,and P11S also have a common structural character of six-coordinated octahedral networks;however,their bonding unsaturation are distinct due to the different valence electron numbers and unequal ratios of P and S atoms.These features provide an ideal model for exploring the bonding-unsaturation dependence of superconductivity.We estimated the average bonding unsaturation of these P-rich compounds based on the valence electron numbers and the coordination numbers of the central P/S atoms.Interestingly,the resultant average bonding unsaturation was found to be proportional to the predicted superconducting transition temperature.This finding was also verified in MH9(M=Y,Th,and Pr)and doped H3S(Si,C,and P)compounds.Our work provides an opportunity to gain a deeper understanding of bonding-unsaturation-dependent superconductivity.