Superconductivity in metastable phases of phosphorus-hydride compounds under high pressure

Recently, compressed phosphine was reported to metallize at pressures above 45\,GPa, reaching a superconducting transition temperature (T$_{c}$) of 100\,K at 200\,GPa. However, neither the exact composition nor the crystal structure of the superconducting phase have been conclusively determined. In this work the phase diagram of PH$_n$ ($n=1,2,3,4,5,6$) was extensively explored by means of {\it ab initio} crystal structure prediction methods. The results do not support the existence of thermodynamically stable PH$_n$ compounds, which exhibit a tendency for elemental decomposition at high pressure even when vibrational contributions to the free energies are taken into account. Although the lowest energy phases of PH$_{1,2,3}$ display T$_{c}$'s comparable to experiments, it remains questionable if the measured values of T$_{c}$ can be fully attributed to a phase-pure compound of PH$_n$.