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

Abstract

Here we report the in situ high-pressure (up to $\ensuremath{\sim}50$-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 $\ensuremath{\sim}17.2$ 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 ${T}_{C}$ at 18.8 GPa is associated with a Lifshitz transition.