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 ${\mathrm{Li}}_2{\mathrm{MgH}}_{16}$.

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• Diffusion
• Electron-phonon coupling
• Electronic structure
• Pressure effects
• Superconducting phase transition
• High-temperature superconductors
• Hydrides
• First-principles calculations
• Methods in superconductivity
• Path-integral methods