Electron-hole balance and the anomalous pressure-dependent superconductivity in black phosphorus

Here we report the first in-situ high pressure (up to ~ 50 GPa) Hall effect measurements on single crystal black phosphorus. We find a strong correlation between the sign of the Hall coefficient, an indicator of the dominant carrier type, and the superconducting transition temperature (T_C). Importantly, we find a change from electron-dominant to hole-dominant carriers in the simple cubic phase of phosphorus at a pressure of ~17.2 GPa, providing an explanation for the puzzling valley it displays in its superconducting T_C vs. pressure phase diagram. Our results reveal that hole-carriers play an important role in developing superconductivity in elemental phosphorus, and the valley in T_C near 17.2 GPa is associated with a Lifshitz transition.