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

Here we report the 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 (TC). 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 TC vs pressure phase diagram. Our results reveal that hole carriers play an important role in developing superconductivity in elemental phosphorus and the valley in TC at 18.8 GPa is associated with a Lifshitz transition.