Superconductivity in black phosphorus and the role of dynamical screening

TL;DR

This paper investigates the superconductivity of cubic phosphorus under pressure, highlighting the importance of dynamical screening and many-body effects in accurately predicting the critical temperature.

Contribution

It introduces a comprehensive density functional theory approach incorporating dynamical screening and GW corrections to better explain experimental $T_c$ values.

Findings

Full frequency-dependent screening improves $T_c$ predictions.

Static electronic contributions underestimate $T_c$.

Quasi-particle band modifications enhance high-pressure $T_c$.

Abstract

Simple cubic phosphorus exhibits superconductivity with a maximum $T_c$ of up to 12 K under pressure. The pressure dependence of $T_c$ cannot be consistently explained with a simple electron-phonon 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 $T_c$, 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 $T_c$ 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 $T_c$ in the high-pressure region.