Topological electride phase of sodium at high pressures and temperatures
Busheng Wang, Katerina P. Hilleke, Xiaoyu Wang, D. N. Polsin, Eva Zurek
Abstract
Sodium, a textbook example of a nearly-free-electron metal, exhibits unforeseen pressure-induced behavior including the stabilization of numerous polymorphs---some possessing extremely complex unit cells---as well as a metal-to-insulator transition to the iconic $hP4$ phase. However, until recently, most of the experimental and theoretical studies on solid sodium have been restricted to the low-temperature regime. Herein, using ab initio evolutionary structure searches coupled with quasiharmonic calculations, we discover seven new phases of sodium that are more stable than the known $hP4$ phase at pressure-temperature conditions that were recently attained in ramp-compression experiments. From these, our calculations suggest that $\mathit{P}{6}_{3}/\mathit{m}$ Na is the ground state between $\ensuremath{\approx}250$ GPa at 710 K and $\ensuremath{\approx}350$ GPa at 1900 K. Electronic structure calculations show that this phase is a topological semimetal with a Dirac nodal surface that is protected by a nonsymmorphic symmetry ${S}_{2z}$ and an electride owing to its non-nuclear charge localized within one-dimensional honeycomb channels and zero-dimensional cages. Our results highlight the complexity of dense sodium's free-energy landscape and intricate electronic structure that emerges at finite temperatures and conditions where ionic cores overlap.