Predicted Pressure-Induced Superconducting Transition in Electride ${\mathrm{Li}}_6\mathrm{P}$

Electrides are unique compounds where most of the electrons reside at interstitial regions of the crystal behaving as anions, which strongly determines its physical properties. Interestingly, the magnitude and distribution of interstitial electrons can be effectively modified either by modulating its chemical composition or external conditions (e.g., pressure). Most of the electrides under high pressure are nonmetallic, and superconducting electrides are very rare. Here we report that a pressure-induced stable ${\mathrm{Li}}_6\mathrm{P}$ electride, identified by first-principles swarm structure calculations, becomes a superconductor with a predicted superconducting transition temperature $T_c$ of 39.3 K, which is the highest among the already known electrides. The interstitial electrons in ${\mathrm{Li}}_6\mathrm{P}$, with dumbbell-like connected electride states, play a dominant role in the superconducting transition. Other Li-rich phosphides, ${\mathrm{Li}}_5\mathrm{P}$, ${\mathrm{Li}}_{11}{\mathrm{P}}_2$, ${\mathrm{Li}}_{15}{\mathrm{P}}_2$, and ${\mathrm{Li}}_8\mathrm{P}$, are also predicted to be superconducting electrides, but with a lower $T_c$. Superconductivity in all these compounds can be attributed to a combination of a weak electronegativity of phosphorus (P) with a strong electropositivity of lithium (Li), and opens up the interest to explore high-temperature superconductivity in similar binary compounds.

Figure 1

Relative thermodynamic stability of ${\mathrm{Li}}_x{\mathrm{P}}_y$ at 0 K and different pressures (100, 200, and 300 GPa). (a) The calculated formation enthalpy per atom of ${\mathrm{Li}}_x{\mathrm{P}}_y$ compounds with respect to elemental Li and P solids. The thermodynamically stable compounds are shown by solid symbols, connected by the solid line (convex hull). (b) Pressure-composition phase diagram of ${\mathrm{Li}}_x{\mathrm{P}}_y$ compounds.

Figure 2

Structural features of stable Li-P phases at high pressures. (a) $P4/mmm$ LiP at 200 GPa. (b) $C2/c$ ${\mathrm{Li}}_5\mathrm{P}$ at 200 GPa. (c) $Cmcm$ ${\mathrm{Li}}_5\mathrm{P}$ at 300 GPa. (d) $P\text{−}1$ ${\mathrm{Li}}_6\mathrm{P}$ at 200 GPa. (e) $C2/c$ ${\mathrm{Li}}_6\mathrm{P}$ at 300 GPa. (f) $C2/c$ ${\mathrm{Li}}_8\mathrm{P}$ at 200 GPa. In all these structures, green and orange spheres represent Li and P atoms, respectively.

Figure 3

Electronic and superconducting properties of $C2/c$ ${\mathrm{Li}}_6\mathrm{P}$. (a) Difference charge density (crystal density minus superposition of isolated atomic densities) for $C2/c$ ${\mathrm{Li}}_6\mathrm{P}$ plotted on the ($01/30$) plane at 300 GPa. (b) The nested Fermi surface along the $\mathrm{\Gamma }\to M$ direction for $C2/c$ ${\mathrm{Li}}_6\mathrm{P}$. The Fermi surface of each band crossing the Fermi energy is shown in Fig. S8 of Ref. [59]. (c) The electronic band structure of $C2/c$ ${\mathrm{Li}}_6\mathrm{P}$ at 300 GPa. (d) PDOS of $C2/c$ ${\mathrm{Li}}_6\mathrm{P}$ at 300 GPa. The red line labeled by “inter” is obtained by projecting onto the interstitial orbitals (interstitial-site-centered spherical harmonics in empty spheres with a Wigner-Seitz radius of 1.0 Å). (e) Eliashberg spectral function (orange area) and frequency-dependent electron-phonon coupling parameters $\lambda (\omega )$ (blue line) of $C2/c$ ${\mathrm{Li}}_6\mathrm{P}$ at 270 GPa. (f) The electron-phonon coupling coefficient $\lambda$ (black dashed line) and the logarithmic average phonon frequency ${\omega }_{\log }$ (red dashed line) as a function of pressure. The critical temperature $T_c$ (blue line) as a function of pressure is shown in the inset. The calculated phonon dispersion curves of $C2/c$ ${\mathrm{Li}}_6\mathrm{P}$ at 300 (g), and 200 GPa (h). The area of each circle is proportional to the partial electron-phonon coupling, ${\lambda }_{q,v}$.