Coexistence of Superconductivity and Superionicity in Li${}_2$MgH${}_{16}$

We study superconductivity in the superionic phase of the clathrate hydride Li${}_2$MgH${}_{16}$, where hydrogen ions diffuse among the lattice formed by lithium and magnesium ions. By employing the stochastic path-integral approach, we non-perturbatively take into account the effects of quantum diffusion and anharmonic vibrations. Our calculations reveal strong electron-ion coupling ($\lambda (0)$ = 3.7) and a high superconducting transition temperature ($T_c$) 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 Li${}_2$MgH${}_{16}$.