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We study superconductivity in the superionic phase of the clathrate hydrideLi$_2$MgH$_{16}$, where hydrogen ions diffuse among the lattice formed bylithium and magnesium ions. By employing the stochastic path-integral approach,we non-perturbatively take into account the effects of quantum diffusion andanharmonic 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. $T_c$ issignificantly suppressed compared with the result $T_c$ = 473 K obtained fromthe conventional approach based on the harmonic approximation. Our study, basedon a first-principles approach applicable to superionic systems, indicates thatthe superconductivity and superionicity can coexist in Li$_2$MgH$_{16}$.

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