Superconductivity in dense scandium-based phosphides

The recent achievement of room-temperature superconductivity at near-ambient pressure in nitrogen-doped lutetium hydride further boosts enthusiasm for the pursuit of high-temperature superconductors. Transition-metal phosphides (TMPs) have attracted substantial attention due to their fascinating properties encompassing superconductivity. Nevertheless, the superconducting scandium-based phosphides with high scandium concentration are not well comprehended. Towards this end, our work focuses on the rational design of scandium-rich phosphides via the first-principles swarm structure calculations under pressure. Strikingly, several metallic phases, viz., ScP, ${\mathrm{Sc}}₂\mathrm{P}$, and ${\mathrm{Sc}}₃\mathrm{P}$, are unambiguously uncovered wherein P atoms exhibit captivating configurations from ladder, linear chain, and eventually to isolated atom. Further electron-phonon coupling simulations elucidate that $P6/mmm {\mathrm{Sc}}₂\mathrm{P}$, isostructural to $\mathrm{Mg}{\mathrm{B}}₂$, possesses a remarkable superconducting transition temperature, ${T}_c$, of $\ensuremath{\sim}20$ K at 100 GPa, mainly deriving from the large acoustic phonon softening in the low-frequency region. Tetragonal $I4/mmm {\mathrm{Sc}}₃\mathrm{P}$ is revealed to host a high phonon-mediated superconductivity of 20.5 K at 140 GPa, which is chiefly attributed to the significant coupling between the low-frequency softened acoustic and optical phonon modes associated with the Sc-dominated vibrations and Sc $3d$ electronic states around the Fermi energy. This study paves the way for discovering distinguished superconductors in transition metal-based phosphide systems.