Thermal effects on the electronic properties of sodium electride under high pressures

Sodium is a simple metal at ambient conditions, while it transits to an electride phase at pressures above \ensuremath{\sim}160 GPa along the room-temperature isotherm. We explore the thermal effects on the electronic properties of the $\mathit{hP}4$ phase of sodium along the $\ensuremath{\rho}=5.872\phantom{\rule{0.16em}{0ex}}\mathrm{g}/\mathrm{c}{\mathrm{m}}³$ isochore. We quantitatively classify this phase as an insulator based on the criterion of nearsightedness of the one-particle density matrix. Ab initio calculations suggest that the band gap of this insulator decreases with increasing temperature along the isochore, primarily because of ionic distortions, culminating in an insulator-to-metal transition upon melting at ${T}_m\ensuremath{\approx}2100\phantom{\rule{0.16em}{0ex}}\mathrm{K}$. This transition is accompanied by residual electronic localization (in $d$ orbitals) in the form of dynamic electron bubbles and a change in hybridization from p-d to s-p upon melting. This transition is explored by tracking the electronic and electro-optical properties along the isochore under consideration.