Exceptional hardness and superconductivity of sp3-hybridized boron frameworks encapsulating actinium at ambient pressure

Recent investigations into layered and clathratelike binary polyborides drive us to explore the crystal structures and associated properties of Ac-B compounds through first-principles calculations in combination with crystal structure prediction techniques. Electron transfer from Ac to B gives rise to the emergence of $s{p}^{3}$-hybridized B frameworks with centered Ac atoms, namely Ac at ${\mathrm{B}}_{24}$ cages in ${\mathrm{AcB}}_{6}$, Ac at ${\mathrm{B}}_{26}$ cages in ${\mathrm{AcB}}_{8}$, and Ac at semiclosed ${\mathrm{B}}_{24}$ units in ${\mathrm{AcB}}_{12}$. Research unveils that three B-based compounds can stabilize at ambient pressure and exhibit inherent incompressibility with Vickers hardness of $22\ensuremath{\sim}38\phantom{\rule{0.16em}{0ex}}\phantom{\rule{0.16em}{0ex}}\mathrm{GPa}$. Intriguingly, the rigid ${\mathrm{AcB}}_{8}$ and ${\mathrm{AcB}}_{12}$ are identified as ambient-pressure superconductors with superconducting transition temperatures (${T}_{c}\mathrm{s}$) of 27 and 8 K, respectively. In particular, based on the Migdal-Eliashberg theory, the ambient-pressure superconductivity of clathratelike ${\mathrm{AcB}}_{8}$ is characterized as single gap and anisotropic, originating from the coupling of $\mathrm{B}\text{\ensuremath{-}}2p$ orbitals states with all phonon modes. Our work not only provides significant guidance for studying anisotropic superconductivity in other clathratelike polyborides but also lays the foundation for seeking and designing superconducting materials with superior hardness in rare-metal borides.