High-temperature superconductivity of boron-carbon clathrates at ambient pressure

The successful synthesis of the carbon-boron clathrate ${\mathrm{SrB}}_3{C}_3$ under high-pressure conditions of 50 GPa opens up a new possibility for exploring high-temperature superconductors at ambient pressure. Based on the first-principle calculation, we designed a class of ${\mathrm{LaH}}_{10}$-like clathrate compounds $\mathrm{Fm}\overline{3}m-X{B}_2{C}_8$ ($X$ = K, Rb, Cs, Sr, Ba, Ga, In, Tl, Sn, Pb, and Bi) and investigate their physical properties and potential superconductivities. Our calculations reveal that the dynamic stability of $\mathrm{Fm}\overline{3}m-X{B}_2{C}_8$ at ambient pressure is determined by the degree of compatibility between the host metal $X$ and the carbon-boron sublattices. Especially, $p$ orbitals of the $p$-region metals can enhance the interaction of the guest atoms with B-C cages, which results in maintaining these clathrates as dynamically stable. Moreover, altering the oxidation states of the guest atoms can adjust the electronic density of states near the Fermi surface, which in turn affects the superconducting transition temperatures ($T_c$'s) of these compounds. Herein, when filled with $+1$ oxidation state metals, the $T_c$'s of $X{B}_2{C}_8$ ($X$ = K, Rb, Cs, Ga, In, and Tl) all exceed the liquid-nitrogen boiling point of 77 K and the $T_c$ of ${\mathrm{TlB}}_2{C}_8$ is expected to reach 96 K at ambient pressure, which is the highest among the studied carbon-boron compounds.