Hexagonal supertetrahedral gallium: a cluster-based three-dimensional topological metal

Two novel three-dimensional allotropes, designated as hexagonal supertetrahedral aluminum and gallium (h-Al/h-Ga), are proposed based on a hexagonal diamond structure and share the same space group symmetry (P6₃/mmc) as hexagonal diamond. First-principles calculations demonstrate their structural stability and superior mechanical properties. Notably, these allotropes exhibit distinct electronic characteristics: h-Al behaves as a narrow-bandgap semiconductor, while h-Ga manifests as a topological semimetal with multiple band crossings. We systematically investigate the topological characteristics of h-Ga, which hosts three distinct classes of topological states: triple point, nodal line, and nodal surface, with associated Fermi arcs and drumhead-like surface states. Furthermore, the inclusion of spin-orbit coupling lifts all topological degeneracies, driving a phase transition to a Dirac semimetal. Our findings not only contribute to the expansion of the supertetrahedral materials family but also underscore hexagonal supertetrahedral lattices as a robust and versatile platform for the discovery of diverse topological phases.