Isotope effect in superconducting lanthanum hydride under high compression

Recently, the discovery of room-temperature superconductivity (SC) was experimentally realized in the fcc phase of ${\mathrm{LaH}}_{10}$ under megabar pressure. Specifically, the isotope effect of $T_{\mathrm{c}}$ was measured by the replacement of hydrogen (H) with deuterium (D), demonstrating a driving role of phonons in the observed room-temperature SC. Herein, based on the first-principles calculations within the harmonic approximation, we reveal that (i) the identical electron-phonon coupling constants of fcc ${\mathrm{LaH}}_{10}$ and ${\mathrm{LaD}}_{10}$ decrease monotonously with increasing pressure and (ii) the isotope effect of $T_{\mathrm{c}}$ 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 at around 150 GPa. Thus, our findings provide a theoretical confirmation of the conventional electron-phonon coupling mechanism in a recently discovered room-temperature superconductor of compressed ${\mathrm{LaH}}_{10}$.