Is sodium a superconductor under high pressure?

Abstract

Superconductivity has been predicted or measured for most alkali metals under high pressure, but the computed critical temperature (T) of sodium (Na) at the face-centered cubic (fcc) phase is vanishingly low. Here we report a thorough, first-principles investigation of superconductivity in Na under pressures up to 260 GPa, where the metal-to-insulator transition occurs. Linear-response calculations and density functional perturbation theory were employed to evaluate phonon distributions and the electron-phonon coupling for bcc, fcc, cI16, and tI19 Na. Our results indicate that the maximum electron-phonon coupling parameter, λ, is 0.5 for the cI16 phase, corresponding to a theoretical peak in the critical temperature at T≈1.2 K. When pressure decreases or increases from 130 GPa, T drops quickly. This is mainly due to the lack of p-d hybridization in Na even at 260 GPa. Since current methods based on the Eliashberg and McMillian formalisms tend to overestimate the T (especially the peak values) of alkali metals, we conclude that under high pressure-before the metal-to-insulator transition at 260 GPa-superconductivity in Na is very weak, if it is measurable at all.

A First-Principles Exploration of NaxSy Binary Phases at 1 atm and Under Pressure

“…Remarkably, as first predicted by theory [88], sodium undergoes a metal to insulator (MIT) transition by 200 GPa, which results from the overlap of core electrons and the concomitant localization of p − d hybridized valence electrons, which render this phase an electride [61]. Theoretical calculations have found that the maximum electron-phonon-coupling parameter, λ, for sodium occurs for the cI16 phase near 140 GPa [89]. Estimates of the T c within the Allen-Dynes modified McMillan equation and µ * = 0.13 found a maximum T c of 1.2 K, leading to the conclusion that superconductivity in sodium prior to the MIT is weak or non-existent.…”