Pressure dependence of superconductivity in simple cubic phosphorus

Abstract

The electronic structure and lattice dynamics for simple cubic (sc) P are calculated over the pressure range 0--70 GPa from first principles using the local-density approximation. The $R$ phonon mode is found to be unstable below 20 GPa in the harmonic approximation, but may be stable down to a pressure less than 20 GPa when anharmonicity is considered. The electron-phonon coupling is calculated for pressures above 20 GPa, and the superconducting transition temperature ${T}_{c}$ is found to decrease with increasing pressure throughout this pressure range. The result is in agreement with experimental results above 30 GPa. In contrast to experiment, no evidence for a decrease in ${T}_{c}$ with decreasing pressure below 30 GPa is found. The structural transition from rhombohedral $A7$ to sc is also investigated. An interesting two-step transition is found to occur theoretically which may have relevance for the pressure dependence of ${T}_{c}$. Possible explanations for the discrepancy with experiment are discussed.