Pressure-induced superconductivity in Li-Te electrides

Electrides, which accommodate excess of electrons in lattice interstitials as anions, usually exhibit interesting properties and broad applications. Until now, most electrides, especially at high pressures, show semiconducting/insulating character arising from the strong localization of interstitial and orbital electrons. However, modulating their connectivity could turn them into metals and even superconductors. In this work, with the aid of first-principles particle swarm optimization, we have identified a series of pressure-induced Li-rich electrides in the Li-Te system, in which hollow ${\mathrm{Li}}_n$ polyhedra accommodate the excess of electrons. With increasing Li content, these electrides undergo an interesting structural evolution. Meanwhile, the connection type of ${\mathrm{Li}}_n$ polyhedra experiences transitions from vertex- or edge sharing, to face sharing, leading to a diverse distribution and connectivity of interstitial electrons. All identified electrides exhibit anionic electrons-dominated metallicity. More interestingly, ${\mathrm{Li}}_9\mathrm{Te}$, with the highest content of ${\mathrm{Li}}_6$ octahedra, is superconducting with a critical temperature $\left(T_{\mathrm{c}}\right)$ of 10.2 K at 75 GPa, which is much higher than typical electrides (e.g., $12\mathrm{CaO}·7{\mathrm{Al}}_2{\mathrm{O}}_3$, ${\mathrm{Ca}}_2\mathrm{N}$, and ${\mathrm{Y}}_2\mathrm{C}$). Its superconductivity mainly originates from the coupling between hybridized electrons (anionic and atomic non-$s$-state ones) and Te-dominated phonons.

Figure 1

(a) Phase stabilities of various Li-Te compounds at 0, 25, 50, and 100 GPa. The $Fm\text{−}3m$, $I\text{−}43d$, and $Cmca$-24 structures of elemental solid Li were used to calculate the formation enthalpies [60, 61, 62]. Elemental solid Te with phases I ($P{3}_{1}21$), V ($Im\text{−}3m$), VI ($I4/mmm$), and VII ($Fm\text{−}3m$) were used [63]. (b) Schematic illustration of the pressure stability region of Li-Te compounds.

Figure 2

Structural features of stable Li-rich tellurides at high pressures. (a) $Pm\text{−}3m{\mathrm{Li}}_3\mathrm{Te}$ at 50 GPa, (b) $I4/mmm{\mathrm{Li}}_3\mathrm{Te}$ at 100 GPa, (c) $Imma{\mathrm{Li}}_4\mathrm{Te}$ at 50 GPa, (d) $Cmmm{\mathrm{Li}}_5\mathrm{Te}$ at 50 GPa, (e) $P{2}_1/m{\mathrm{Li}}_7\mathrm{Te}$ at 50 GPa, (f) $C2/m{\mathrm{Li}}_9\mathrm{Te}$ at 50 GPa, (g) $C2/m{\mathrm{Li}}_{10}\mathrm{Te}$ at 100 GPa, and (h) $Cmcm{\mathrm{Li}}_{12}\mathrm{Te}$ at 50 GPa. In all these structures, green and purple spheres represent Li and Te atoms, respectively.

Figure 3

ELF maps of Li-rich tellurides at high pressure. (a) $Pm\text{−}3m{\mathrm{Li}}_3\mathrm{Te}$ at 50 GPa in the (110) plane, (b) $I4/mmm{\mathrm{Li}}_3\mathrm{Te}$ at 100 GPa in the (001) plane, (c) $Imma{\mathrm{Li}}_4\mathrm{Te}$ at 50 GPa in the (010) plane, (d) $Cmmm{\mathrm{Li}}_5\mathrm{Te}$ at 50 GPa in the (010) (left) and (001) (right) planes, (e) $P{2}_1/m{\mathrm{Li}}_7\mathrm{Te}$ at 50 GPa in ($hkl=13.978$, 1, 58.75) (left) and ($hkl=1.276$, 0, 1) (right) planes, (f) $C2/m{\mathrm{Li}}_9\mathrm{Te}$ at 50 GPa in ($hkl=-1$, 0, 2.089) (left) and (001) planes, (g) $C2/m{\mathrm{Li}}_{10}\mathrm{Te}$ at 100 GPa in the (101) plane, and (h) $Cmcm{\mathrm{Li}}_{12}\mathrm{Te}$ at 50 GPa in ($hkl=1.853$, 1, 0) (above) and (100) (below) planes.

Figure 4

(a) PDOS of $C2/m{\mathrm{Li}}_9\mathrm{Te}$ at 50 GPa. PHDOS, Eliashberg spectral function, and frequency-dependent electron-phonon coupling parameters $\lambda \left(\omega \right)$ of (b) $C2/m{\mathrm{Li}}_9\mathrm{Te}$ at 50 GPa and (e) $C2/m{\mathrm{Li}}_{10}\mathrm{Te}$ at 100 GPa. (c) The calculated phonon dispersion curves of $C2/m{\mathrm{Li}}_9\mathrm{Te}$ at 75 GPa. The area of each circle is proportional to the partial electron-phonon coupling, ${\lambda }_{q,v}$. (d) Pressure-dependent $\lambda \left(\omega \right)$, ${\omega }_{log}$, and $T_{\mathrm{c}}$ of $C2/m{\mathrm{Li}}_9\mathrm{Te}$. (f) The work function of $C2/m{\mathrm{Li}}_{10}\mathrm{Te}$ at 100 GPa. The Fermi level is set to zero. The inset displays the corresponding slab with a thickness of at least ten atoms.