Calculation of electron-phonon coupling in Arsenic under pressure

Elemental As undergoes a structural transformation from a rhombohedral A7 phase to a simple cubic (sc) phase at around 25 GPa as pressure is increased. At pressures near this phase transformation, As is superconducting, with a maximum superconducting transition temperature $T_c$ of about 2.5 $K$. Experiments indicate that this maximum $T_c$ occurs at the transition pressure for structural transformation, and the increase in $T_c$ as the transition pressure is approached has been attributed to phonon softening. In this work, we calculate from first principles the electronic structure, phonon dispersions, and electron-phonon coupling constant $\lambda$ for As in the A7 and sc phases at various pressures near the A7 to sc transition. Using these detailed quantitative calculations, we explain the trends in $T_c$ as function of pressure in terms of phonon softening, electronic density of states, and electron-phonon matrix elements. We discuss the implications of these results for finding new superconducting materials.