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

The successful synthesis of the carbon-boron clathrate ${\mathrm{SrB}}_3{\mathrm{C}}_3$ 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 $\mathit{Fm}\overline{3}m-X{\mathrm{B}}_2{\mathrm{C}}_8$ ($X$ = 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 $\mathit{Fm}\overline{3}m-X{\mathrm{B}}_2{\mathrm{C}}_8$ 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 $X{\mathrm{B}}_2{\mathrm{C}}_8$ ($X$ = K, Rb, Cs, Ga, In, and Tl) all exceed the liquid-nitrogen boiling point of 77 K and the $T_c$ of ${\mathrm{TlB}}_2{\mathrm{C}}_8$ is expected to reach 96 K at ambient pressure, which is the highest among the studied carbon-boron compounds.

Figure 1

(a) The crystal structure of $\mathit{Fm}\overline{3}m-{\mathrm{LaH}}_{10}$. La atoms are shown in green, and two different kinds of H atoms are shown in pink and gray. (b) The crystal structure of $\mathit{Fm}\overline{3}m-X{\mathrm{B}}_2{\mathrm{C}}_8$ ($X=\mathrm{K}$, Rb, Cs, Sr, Ba, Ga, In, Tl, Sn, Pb, and Bi). $X$ atoms are shown in violet, B atoms are shown in cyan, and C atoms are shown in orange. (c) Calculated ELF of $\mathit{Fm}\overline{3}m-{\mathrm{KB}}_2{\mathrm{C}}_8$ at 0 GPa. (d) Periodic table of the stability for $\mathit{Fm}\overline{3}m-X{\mathrm{B}}_2{\mathrm{C}}_8$ at ambient pressure, with columns indicating the major groups of elements and rows indicating periods, where dynamically unstable compounds in phonon calculations at atmospheric pressure are shown in gray and stable compounds are shown in blue.

Figure 2

Isosurface map of interaction region indicator (IRI) of (a) ${\mathrm{CsB}}_2{\mathrm{C}}_8$, (b) ${\mathrm{BaB}}_2{\mathrm{C}}_8$, (c) ${\mathrm{LaB}}_2{\mathrm{C}}_8$, (d) ${\mathrm{TlB}}_2{\mathrm{C}}_8$, (e) ${\mathrm{PbB}}_2{\mathrm{C}}_8$, and (f) ${\mathrm{BiB}}_2{\mathrm{C}}_8$, at 1 atm, using the standard coloring method and chemical explanation of $\mathrm{sign}({\lambda }_2$) $\rho$ on IRI isosurfaces.

Figure 3

Calculated electronic band structures and projected density of states (PDOS) for (a) ${\mathrm{CsB}}_2{\mathrm{C}}_8$, (b) ${\mathrm{BaB}}_2{\mathrm{C}}_8$, (c) ${\mathrm{LaB}}_2{\mathrm{C}}_8$, (d) ${\mathrm{TlB}}_2{\mathrm{C}}_8$, (e) ${\mathrm{PbB}}_2{\mathrm{C}}_8$, and (f) ${\mathrm{BiB}}_2{\mathrm{C}}_8$ at atmospheric pressure by using HSE06 $+$ SOC where the $E_F$ is set to zero. The total densitis of states for B, C, and guest metals projected onto the energy band are shown with blue, red, and green points, respectively.

Figure 4

Calculated superconducting parameters for $\mathit{Fm}\overline{3}m-X{\mathrm{B}}_2{\mathrm{C}}_8$ ($X$ = K, Rb, Cs, Ga, In, Tl, Sn, Pb, and Bi). $T_c$'s calculated by Allen-Dynes-modified equations (${\mu }^{*}=0.1$–0.13), ${\omega }_{\log }, \lambda$, and $N_{EF}$ at the $E_F$. The gray dashed line in the picture is the liquid-nitrogen boiling-point temperature.

Figure 5

Phonon dispersion curves, projected phonon density of states, Eliashberg spectral function scaled by the frequency [${\alpha }^{2}F\left(\omega \right)$], and the EPC integral ($\lambda$) for (a) ${\mathrm{CsB}}_2{\mathrm{C}}_8$, (b) ${\mathrm{TlB}}_2{\mathrm{C}}_8$, (c) ${\mathrm{PbB}}_2{\mathrm{C}}_8$, and (d) ${\mathrm{BiB}}_2{\mathrm{C}}_8$ at 0 GPa. The bubble's radius on the phonon dispersion curve is proportional to the electron-phonon coupling constant ($\lambda$).