Coexistence of Superconductivity and Superhardness in M ₂ B ₄ C ₈ Clathrates at Ambient Pressure

Boron and carbon are light elements with the capacity for forming strong covalent bonds. Their high Debye frequencies give them significant potential as superconducting materials, while their robust covalent bonding also makes them excellent candidates for superhard materials. Through high-throughput structural searches under ambient pressure, we have identified two clathrate-type B4C8 frameworks. Our results indicate that, upon doping with main-group and transition metals, these frameworks yield a series of stable superconductors: M2B4C8–I (M = K, Rb, Bi) with Tc values of 13 K, 17 K, and 5 K, respectively; and M2B4C8–II (M = K, Rb, Cs, Sc, Sb, Tl) with Tc values of 9 K, 27 K, 19 K, 23 K, 16 K, and 6 K, respectively. Notably, K and Rb in both frameworks exhibit superhard characteristics, with the highest Vickers hardness of 51.2 GPa achieved in K2B4C8–I configuration. Our work not only compares and elucidates the origins of superconductivity and superhardness within these two frameworks but also proposes a feasible strategy for designing and synthesizing superhard superconductors under ambient pressure.