Proposed Superconducting Electride ${\mathrm{Li}}_6\mathrm{C}$ by $sp$-Hybridized Cage States at Moderate Pressures

The combination of electride state and superconductivity within the same compound, e.g., ${[{\mathrm{Ca}}_{24}{\mathrm{Al}}_{28}{\mathrm{O}}_6]}^{4+}(4e^{-})$, opens up a new category of conventional superconductors. However, neither the underlying causations to explain superconducting behaviors nor effects of interstitial quasiatoms (ISQs) on superconductivity remain unclear. Here we have designed an efficient and resource-saving method to identify superconducting electrides only by chemical compositions and bonding characteristics. A representative superconducting electride ${\mathrm{Li}}_6\mathrm{C}$ with a noteworthy $T_c$ of 10 K below 1 Mbar among the known binary electrides has been revealed. Our first-principles studies unveil that the anomalous $sp$-hybridized cage-state ISQs, as a guest in ${\mathrm{Li}}_6\mathrm{C}$, exhibit unexpected ionic and covalent bonds, which act as a chemical precompression to lower dynamically stable pressure. More importantly, we uncover that, contrary to common expectations, the high $T_c$ is attributed to the strong electron-phonon coupling derived from the synergy of interatomic coupling effect, phonon softening caused by Fermi surface nesting, and phonon-coupled bands, which are mainly dominated by host $sp$-hybridized electrons, rather than the ISQs. Our present results elucidate a new superconducting mechanism of electrides and shed light on the way for seeking a high-$T_c$ superconductor at lower pressures in cage-state electrides.

Figure 1

Schematic illustrating the proposed calculation-aided methodology for identifying potential electrides.

Figure 2

Formation enthalpies and structural characteristics of ${\mathrm{Li}}_6\mathrm{C}$: (a) Formation enthalpies of predicted phases as a function of pressures. (b) Volume versus pressure for anti-${\mathrm{CdCl}}_2\text{−}\mathrm{I}$ and II phases. (c) The anti-${\mathrm{CdCl}}_2\text{−}\mathrm{I}$ phase at 40 GPa (d) anti-${\mathrm{CdCl}}_2\text{−}\mathrm{II}$ phase at 60 GPa. (e) 3D isosurface (isosurface of 0.85) of ELF and (f) a 2D map of the (110) plane in anti-${\mathrm{CdCl}}_2\text{−}\mathrm{I}$ phase at 40 GPa. (g) 3D isosurface of anti-${\mathrm{CdCl}}_2\text{−}\mathrm{II}\text{−}{\mathrm{Li}}_6\mathrm{C}$ at 60 GPa.

Figure 3

Density of state and bonding characteristics of the anti-${\mathrm{CdCl}}_2\text{−}\mathrm{II}$ phase at 60 GPa: (a) 3D partial charge density maps (isosurface of 0.015), projected density of states (PDOS), and Fermi surfaces for the bands labeled i, ii, and iii; (b) integral DOS values at $E_F$ on a per f.u. basis; (c) calculated ICOHP values and $\mathrm{Li}─\mathrm{Li}$ bond lengths with intervening ISQs and without intervening ISQs under different pressures.

Figure 4

(a) Phonon dispersion, projected phonon DOS, Eliashberg spectral function ${\alpha }^{2}F(\omega )$ with integrated EPC parameter $\lambda (\omega )$ at 60 GPa. Red solid circles represent the phonon linewidth with a radius proportional to the strength. (b) Values of $\lambda$ and $T_c$ as a function of pressures. (c) Fermi surface and 3D and 2D (0.8 0.3–0.3) plane nesting function $\xi (Q)$ calculated with $60\times 60\times 60\mathrm{k}$ mesh in a primitive cell of reciprocal space. (d) $T_c$’s versus pressure for representative superconducting electrides [11, 49, 50, 51]. (e) Contributions of different atoms to the total DOS at the $E_F$.