Coexistence of superconductivity and superionicity in ${\mathrm{Li}}_2{\mathrm{MgH}}_{16}$

We study superconductivity in the superionic phase of the clathrate hydride ${\mathrm{Li}}_2{\mathrm{MgH}}_{16}$, where hydrogen ions diffuse among the lattice formed by lithium and magnesium ions. By employing the stochastic path-integral approach, we nonperturbatively take into account the effects of quantum diffusion and anharmonic vibrations. Our calculations reveal strong electron-ion coupling $\left[\lambda \right(0)=3.7]$ and a high superconducting transition temperature $\left(T_c\right)$ of 277 K under 260 GPa, at which the material is still superionic. $T_c$ is significantly suppressed compared with the result $T_c=473$ K obtained from the conventional approach based on the harmonic approximation. Our study, based on a first-principles approach applicable to superionic systems, indicates that the superconductivity and superionicity can coexist in ${\mathrm{Li}}_2{\mathrm{MgH}}_{16}$.

Figure 1

(a) Mean squared displacement (MSD) of hydrogen (blue solid line), lithium (red dashed line), and magnesium (yellow dot-dashed line) ions under 260 GPa at 290 K. MSD of hydrogen ions from classical MD simulation at 290 K and PIMD simulation at 350 K are also shown for comparison. (b) [100] view of trajectories of centroid mode of all hydrogen (gray), lithium (red), and magnesium (yellow) ions. Selected trajectories of hydrogen ions are marked by blue lines. (c) [100] view of density distribution of hydrogen ions from a PIMD simulation. Hydrogen ions of the solid phase are marked with cross marks. (d) The effective “crystal structure” of the superionic phase. The structure is made up of three basic components: ${\mathrm{Li}}_4$ (gray), ${\mathrm{Li}}_3\mathrm{Mg}$ (yellow), and ${\mathrm{Li}}_2{\mathrm{Mg}}_2$ (green) tetrahedra, with hydrogen ions occupying their centers. (e) A schematic illustration of the effective structural transition around the ${\mathrm{Li}}_4$ tetrahedra from solid phase (left) to superionic phase (right). In the right panel, the previously empty 8b site is circled in red solid line.

Figure 2

(a) Partial density of states $\rho (\mathit{k},E)$ in the IBZ calculated under quasistatic approximation (mapped into colors in the background) and band structure solved from the effective Hamiltonian (black solid lines) in the superionic phase. Band structures in the solid phase (red dashed lines) are shown for comparison. (b) DOS in the two states. The superionic one is calculated using eigenvalues from all configurations.

Figure 3

EPC parameters $\lambda \left(m\right)$ of ${\mathrm{Li}}_2\mathrm{MgH}{}_{16}$ under 260 GPa at 290 K, calculated on a $8\times 8\times 8$ $k$ grid and $8\times 8\times 8$ $q$ grid. Inset: the asymptotic behavior of ${\overline{\omega }}_2\left(m\right)=2\pi /\hslash \beta \sqrt{m^2\lambda \left(m\right)/\lambda \left(0\right)}$. The value at infinity ${\overline{\omega }}_2\left(\infty \right)$ gives the EPC-weighted average phonon frequency [12, 45]. The results are calculated using nondiagonal supercells, each containing 304 atoms [39].

Figure 4

Contributions of different types of ion motion to the EPC parameters $\lambda \left(m\right)$ under 260 GPa at 290 K. Inset: full trajectories and diffusion paths of two selected hydrogen ions obtained using a moving-average filter with 250 fs window length. The diffusion contribution ${\lambda }_{\mathrm{dif}}\left(m\right)$ is calculated from all such diffusion paths. The results are calculated in a supercell containing 76 atoms.