Structural Diversity and Superconductivity in S-P-H Ternary Hydrides Under Pressure

Evolutionary structure searches revealed a plethora of stable and low-enthalpy metastable phases in the S-P-H ternary phase diagram under pressure. A wide variety of crystalline structure types were uncovered ranging from those possessing one-dimensional chains, two-dimensional sheets based on S-H or S-P-H square lattices as well as S-H or P-H honeycombs, and cage-like structures. Some of the cage-like structures could be derived from doping the high-pressure high-temperature superconducting $Im\bar{3}m$ H$_3$S phase with phosphorous. Most of the discovered compounds were metallic, however those derived from $Im\bar{3}m$ H$_3$S lattices with low levels of P-doping were predicted to possess the highest superconducting critical temperatures ($T_c$s). The propensity for phosphorous to assume octahedral coordination, as well as the similar radii of sulfur and phosphorous are key to maintaining a high density of states at the Fermi level in $Im\bar{3}m$ S$_{0.875}$P$_{0.125}$H$_3$, whose $T_c$ was estimated to be similar to that of H$_3$S at 200~GPa.