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Recently, the discovery of room-temperature superconductivity (SC) wasexperimentally realized in the fcc phase of LaH$_{10}$ under megabar pressure.Specifically, the isotope effect of $T_{\rm c}$ was measured by the replacementof hydrogen (H) with deuterium (D), demonstrating a driving role of phonons inthe observed room-temperature SC. Herein, based on the first-principlescalculations within the harmonic approximation, we reveal that (i) theidentical electron-phonon coupling constants of fcc LaH$_{10}$ and LaD$_{10}$decrease monotonously with increasing pressure and (ii) the isotope effect of$T_{\rm c}$ is nearly proportional to $M^{-{\alpha}}$ ($M$: ionic mass) with${\alpha}$ ${\approx}$ 0.465, irrespective of pressure. The predicted value of${\alpha}$ agrees well with the experimental one (${\alpha}=0.46$) measured ataround 150 GPa. Thus, our findings provide a theoretical confirmation of theconventional electron-phonon coupling mechanism in a newly discoveredroom-temperature superconductor of compressed LaH$_{10}$.

Isotope effect in superconducting lanthanum hydride under high compression