Elemental Phosphorus: structural and superconducting phase diagram under pressure

Pressure-induced superconductivity and structural phase transitions in phosphorous (P) are studied by resistivity measurements under pressures up to 170 GPa and fully $ab-initio$ crystal structure and superconductivity calculations up to 350 GPa. Two distinct superconducting transition temperature (T$_{c}$) vs. pressure ($P$) trends at low pressure have been reported more than 30 years ago, and for the first time we are able to reproduce them and devise a consistent explanation founded on thermodynamically metastable phases of black-phosphorous. Our experimental and theoretical results form a single, consistent picture which not only provides a clear understanding of elemental P under pressure but also sheds light on the long-standing and unsolved $anomalous$ superconductivity trend. Moreover, at higher pressures we predict a similar scenario of multiple metastable structures which coexist beyond their thermodynamical stability range. Metastable phases of P experimentally accessible at pressures above 240 GPa should exhibit T$_{c}$'s as high as 15 K, i.e. three times larger than the predicted value for the ground-state crystal structure. We observe that all the metastable structures systematically exhibit larger transition temperatures than the ground-state ones, indicating that the exploration of metastable phases represents a promising route to design materials with improved superconducting properties.