Topological electride phase of sodium at high pressures and temperatures

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 P63/m Na is the ground state between ≈250 GPa at 710 K and ≈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 S2z 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.