Structural and Vibrational Properties of D$_3$Se from First Principles: Anharmonic Quantum and Isotope Effects

Hydrogen-rich superconductors have garnered considerable interest following the discovery of hot superconductivity in high pressure H$_3$S, reviving prospects for room temperature superconductors under high-pressures. Using H$_3$Se as a reference system, we investigate the vibrational and superconducting properties of D$_3$Se in the Im\bar{3}m phase across 60-200 GPa by combining first-principles calculations with the stochastic self-consistent harmonic approximation to treat ionic quantum and anharmonic effects. These effects introduce significant renormalization to the phonon spectra and stabilize the lattice down to at least 70 GPa, well below the harmonic prediction of >110 GPa. Ultimately, the phonon renormalizations alter the electron-phonon coupling, introducing a decrease in the superconducting critical temperature by about 3-16 K across the studied pressure range with respect to standard calculations. Including anharmonic phonons within the Migdal-Eliashberg theory yields $T_c \approx 154$ K at 75 GPa (with ${\mu}^* = 0.1$, ${\lambda} = 3.0$), highlighting D3Se as a promising high-Tc superconductor at moderate pressures. Examining the role of anharmonicity in the isotope effect, we find that at 200 GPa it suppresses the isotope coefficient $\alpha$ to 0.29 one third below the harmonic value (0.44) which approaches the BCS limit of 0.5. This dramatic reduction demonstrates that anharmonicity fundamentally governs the isotope effect on this system. The stark discrepancy between anharmonic and harmonic descriptions underscores the need for targeted experimental efforts to resolve the origin of the persistent theory-experiment discrepancy in compressed hydrides.