Competing phases, strong electron-phonon interaction, and superconductivity in elemental calcium under high pressure

The observed simple cubic (sc) phase of elemental Ca at room temperature in the 32-109 GPa range is, from linear-response calculations, dynamically unstable. By comparing first-principles calculations of the enthalpy for five sc-related (nonclose-packed) structures, we find that all five structures compete energetically at room temperature in the 40-90 GPa range, and three do so in the 100-130 GPa range. Some competing structures below 90 GPa are dynamically stable, i.e., no imaginary frequency, suggesting that these sc-derived short-range-order local structures exist locally and can account for the observed (average) sc diffraction pattern. In the dynamically stable phases below 90 GPa, some low-frequency phonon modes are present, contributing to strong electron-phonon coupling as well as arising from the strong coupling. Linear-response calculations for two of the structures over 120 GPa lead to critical temperatures in the 20-25 K range as is observed, and do so without unusually soft modes.