First-principles study on the high-$T_\text{c}$ superconductivity of Mg-Ti-H ternary hydrides up to the liquid-nitrogen temperature range under high pressures

Abstract: Ternary hydrides have emerged as the primary focus of the new wave of research into superconducting hydrides. In this work, Mg-Ti-H ternary hydrides are explored under high pressures up to 300 GPa using the prediction method of the particle swarm optimization algorithm combined with first-principles calculations. Two new structures, $P4/nmm$-MgTiH$6$ and $Pmm2$-Mg$_3$TiH$_6$, are identified to be thermodynamically stable at both 200 GPa and 300 GPa. Thermodynamically stable structures of Mg$_3$TiH${12}$ are also identified, whose space groups are $R3/m$ at 200 GPa and $Pm\bar{3}m$ at 300 GPa, respectively. Among these Mg-Ti-H structures, $P4/nmm$-MgTiH$6$ achieves a record-high $T\text{c}$ of 81.9 K at 170 GPa, exceeding the boiling point of liquid nitrogen. Such a high $T_\text{c}$ is primarily attributed to strong electron-phonon coupling (EPC) driven by low-frequency acoustic phonon modes, with the EPC strength reaching a large value of 1.54. The $T_\text{c}$ of $Pm\bar{3}m$-Mg$3$TiH${12}$ is predicted to be 40 K at 300 GPa. Furthermore, element substitution of Zr(Hf) for Ti achieves considerable enhancement of superconducting properties in our predicted hydrogen-rich and high-symmetric crystal structures, i.e., $P4/nmm$-MgTiH$6$ and $Pm\bar{3}m$-Mg$_3$TiH${12}$. The high pressure required for dynamical stability is lowered to 100 GPa in both $Pm\bar{3}m$-Mg$3$ZrH${12}$ and $Pm\bar{3}m$-Mg$3$HfH${12}$, and to 90 GPa and 120 GPa for $P4/nmm$-MgZrH$6$ and $P4/nmm$-MgHfH$_6$, respectively. Particularly, the electronic structure near the Fermi level is significantly modified in the $P4/nmm$-MgHfH$_6$ phase, and pronounced softening of low-frequency acoustic phonon modes occurs. As a result, the EPC strength is enhanced to 1.72, leading to a higher $T\text{c}$ of 86 K.