Potential high-$T_c$ superconductivity in ${\mathrm{CaYH}}_{12}$ under pressure

The high-pressure phases and superconductivity of ${\mathrm{CaYH}}_{12}$ have been explored by using a particle swarm optimization structure prediction methodology in combination with first-principles calculations. Our results show that ${\mathrm{CaYH}}_{12}$ becomes stable with a cubic $Fd\overline{3}m$ structure above 170 GPa, where metal atoms form body-centered-cubic (bcc) lattices and hydrogens occupy all the tetrahedral interstices of these bcc lattices, completing sodalitelike cages. The electron-phonon coupling calculations indicate that the $Fd\overline{3}m$ structure is a potential high-temperature superconductor, with a calculated $T_c$ of 258 K at 200 GPa. Our current study provides a possibility for searching new high-$T_c$ superconductors in ternary hydrides.

Figure 1

The upper panel shows the predicted (a) $Pm\overline{3}m$ and (b) $Fd\overline{3}m$ structures of ${\mathrm{CaYH}}_{12}$ at 200 GPa. The blue, magenta, and dark green atoms represent Ca, Y, and H atoms, respectively. The lower panel shows the calculated enthalpies per formula unit of various structures for ${\mathrm{CaYH}}_{12}$ as a function of pressure with respect to the $Pm\overline{3}m$ structure. The decomposition enthalpies for ${\mathrm{CaYH}}_{12}$ to ${\mathrm{CaH}}_6\left(Im\overline{3}m\right)+{\mathrm{YH}}_6\left(Im\overline{3}m\right)$ and ${\mathrm{CaH}}_4(I4/mmm)+{\mathrm{YH}}_3\left(Fm\overline{3}m\right)+{\mathrm{H}}_2(C2/c)$ are also presented. Inset: Enthalpies of various structures relative to the $Pm\overline{3}m$ structure including zero-point corrections as a function of pressure.

Figure 2

ELF and electronic band structure. The calculated ELF of (a) $Fd\overline{3}m{\mathrm{CaYH}}_{12}$, (b) $Im\overline{3}m{\mathrm{CaH}}_6$, and (c) $Im\overline{3}m{\mathrm{YH}}_6$ with an isosurface value of 0.5 at 200, 150, and 120 GPa, respectively. The lower panels (d)–(f) show electronic band structures corresponding to the structures in the upper panel.

Figure 3

Calculated phonon band structure for $Fd\overline{3}m{\mathrm{CaYH}}_{12}$ at 200 GPa (a). Red solid circles show the phonon linewidth with a radius proportional to the strength. (b) show Ca, Y, and H contributions to the phonon DOS. The Eliashberg phonon spectral function ${\alpha }^{2}F\left(\omega \right)$ and the partial electron-phonon integral $\lambda \left(\omega \right)$ are in (c).

Figure 4

Pressure dependence of $T_c$, calculated within the corrected Allen-Dynes modified McMillan equation, and the electron-phonon coupling parameter $\lambda$ for the $Pm\overline{3}m$ structure. The inset shows the evolution of the logarithmic average frequency ${\omega }_{\text{log}}$ with pressure.