Evidence of Phonon-Mediated Superconductivity in LaH₁₀ at High Pressure

Motivated by the recent experimental discovery of the high-critical-temperature superconductor LaH₁₀ (250–260 K at high pressures 170–190 GPa), the influence of H isotope substitution on the phonon spectra, electron–phonon interactions, and thermodynamic properties of superconducting LaH${}_{10-x}$D_x ($x=0,2,5,8,10$) at 250 GPa are studied. On the basis of first-principles calculations, it is found that all investigated systems are dynamically stable in a clathrate structure with space group Fm$\overline{3}$m and exhibit high superconducting critical temperatures $T_{\mathrm{c}}$ ranging from 169 to 234 K. The dominant role of hydrogen in enhancing $T_{\mathrm{c}}$ is examined by numerically solving the Eliashberg equations. The estimated critical temperature, superconducting energy gap, specific heat, and thermodynamic critical field demonstrate that the underlying mechanism of superconductivity in lanthanum hydride is conventional electron–phonon coupling, which manifests itself in terms of isotope effect.