Superconductivity in black phosphorus and the role of dynamical screening

Abstract

Simple cubic phosphorus exhibits superconductivity with a maximum Tc of up to 12 K under pressure. The pressure dependence of Tc cannot be consistently explained with a simple electronphonon mechanism, which has stimulated investigations into the role of electronic correlations and plasmonic contributions. Here, we solve the gap equation of density functional theory for superconductors using different electron-electron and electron-phonon contributions to the kernel. We find that the phonon contribution alone yields an overestimation of Tc, while the addition of the static electronic contribution results in an underestimation. Taking into account the full frequency dependence of the screened interaction, the one-shot GW approximation predicts Tc values in good agreement with the experiments in the pressure range appropriate for the cubic phase. We also explore the use of quasi-particle bands in the calculation of the electronic and phononic kernels, and show that this modification significantly improves Tc in the high-pressure region.