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

Abstract

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 principle calculations of the enthalpy for five sc-related (non-close-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 (EP) 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.

Stability of simple cubic calcium at high pressure: A first-principles study

“…The diffraction patterns for these structures are even distinctly more different from that of the sc structure. This observation does not therefore provide support for a previous suggestion 17 that, at room temperature, the observed sc phase is an average structure of several competing structures although it is possible that energetically very close structures not yet considered could be contributing.…”

“…Moreover, Yao et al 15 and Oganov et al 16 also predicted the existence of a lower enthalpy I4 1 / amd phase at low temperature. Very recently, Yin et al 17 provided another interpretation along this line. They assumed that since the proposed models are energetically and structurally very close to sc, the observed "sc" phase could be interpreted as a highly anharmonic phase derived from a spatially inhomogeneous and dynamically fluctuating combination of multiple structures.…”

Interplay between structure and superconductivity: Metastable phases of phosphorus under pressure

“…The excellent agreement between our experimental and theoretical results allowed us to not only reconcile previous unexplained anomalies, but also to shed light onto the complex behavior of metastable phases under pressure. Elemental phosphorus, like other elements [53] and compounds [54], has the tendency to form many polymorphs that differ substantially in their electronic and superconducting properties and can coexist in metastable forms over different pressures. In this work, we showed that many of these exhibit critical temperatures which are distinctively higher than the putative ground-state structures.…”

Yaoet al.Reply:

“…Further studies, which require the use of more accurate methods and measurements are necessary. Fluctuations and distortions at finite-temperature among several quasidegenerate structures, as proposed in [8], also need to be considered. …”