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.