H$_{3}$Se in the $Im\overline{3}m$ Phase: A High-Pressure Superconductor with $T_{\text{c}}$ Reaching 200 K at 64 GPa Mediated by Anharmonic Phonons

Abstract Hydrogen-based compounds have attracted significant attention in recent years due to the discovery of conventional superconductivity with high critical temperature under high pressure, rekindling hopes for searching room temperature superconductor. In this work, we investigated systematically the vibrational and superconducting properties of H$_{3}$Se in $Im\overline{3}m$ phase under pressures ranging from 50 to 200 GPa. Our approach combines the stochastic self-consistent harmonic approximation with first-principles calculations to address effects from the quantum and anharmonic vibrations of ions. It turns out that these effects significantly modify the crystal structure, increasing the inner pressure by about 8 GPa compared to situations where they are ignored. The phonon spectra suggest that with these effects included, the crystal can be stabilized at pressures as low as about 61 GPa, much lower than the previously predicted value of over 100 GPa. Our calculations also highlight the critical role of quantum and anharmonic effects on the electron-phonon coupling properties. Neglecting these factors could result in a substantial overestimation of the superconducting critical temperature $T_{\text{c}}$, by approximately 25 K at 125 GPa, for example. With anharmonic phonons, the $T_{\text{c}}$ derived from the Migdal-Eliashberg equations, reaches 200 K ($\mu^\star=0.1, \lambda$=4.1) as the pressure decreases to 64 GPa, making the crystal a rare high-$T_{\text{c}}$ superconductor at moderate pressures.