Borides represent a unique category of materials with potential superconductivity and high hardness. Motivated by recent progresses, we conducted thorough searches in a yttrium-boron binary system employing the first-principles density functional theory. Four superconducting yttrium borides have been identified, including ${\mathrm{YB}}_5$ (Pmma) and ${\mathrm{YB}}_8$ ($R\overline{3}m$) of boron clathrate structures with superconducting transition temperatures $T_{\text{c}}$ = 30.5 K at 20 GPa and 19.9 K at the ambient pressure, respectively. The superconductivity in yttrium-boron superconductors originates from the coupling of B-$2p$ electrons to boron vibrational modes and Y-$4d$ electrons to their atomic vibrations. By high-throughput screening of isostructural ${X\mathrm{B}}_8$ ($R\overline{3}m$) borides in which yttrium is replaced by atoms in the periodic table, we have identified four groups of unprecedented superconductors including ${\mathrm{PbB}}_8$ with $T_{\text{c}}$ = 45.5 K at the ambient pressure. We found ${\mathrm{YB}}_3$ (Cmcm) with boron cages has high Vickers hardness value of 35.2 GPa. By screening of ${X\mathrm{B}}_3$ (Cmcm) isostructures, we also identified a series of unprecedented high-hardness borides. Therefore, our discoveries suggest the enormous potentials of borides with clathrate structures in exploring materials of high superconducting transition temperatures and high hardness at the ambient pressure.

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• Electron-phonon coupling
• Hardness
• Superconductivity
• Borides
• Clathrates
• Density functional calculations