Non-monotonic evolution of superconductivity in phosphorus under high pressure: a first-principles study

Through first-principles calculations, we comprehensively elucidate the non-monotonic variation of the superconducting transition temperature (T_c) of phosphorus (P) over 0-400 GPa. By comparing structural distortions, elastic modulus softening, and the evolution of electronic density of states across pressure phases, alongside electron-phonon coupling analysis, we ascertain that $P6/mmm$ at 80 GPa, a layer phase transition triggers low-frequency phonon softening and resonance with the p-orbital van Hove singularity, culminating in a T_c of 18.3 K. With increasing pressure, systematic hardening of the phonon spectrum reduces the electron-phonon coupling constant (λ). Consequently, $I\overline{4}3d$ at 400 GPa, T_c sharply decreases to 3.5 K. The T_c fluctuation primarily stems from the interplay between λ and TDOS near the Fermi level. This discovery offers new opportunities for exploring high-pressure superconductor characteristics and enhances understanding of electronic structure-lattice dynamics interplay under extreme conditions.

Electronic properties were computed using density functional theory (DFT) in CASTEP; the exchange-correlation interaction is described using the PBE functional within the generalized gradient approximation (GGA). Electron-phonon coupling and superconducting properties were calculated using QUANTUM ESPRESSO with optimized norm-conserving Vanderbilt pseudopotentials (ONCVPSP).