Phase diagrams and superconductivity of ternary Na-Al-H compounds at high pressure

Invigorated by the high-temperature superconductivity in ternary hydrogen-dominated compounds under high pressures, we systematically explored high-pressure phase diagrams, electronic properties, lattice dynamics, and superconductivity of ternary Na-Al-H systems using ab initio methods. We found three stable compounds of ${\mathrm{NaAlH}}_{4}$, ${\mathrm{NaAlH}}_{6}$, and ${\mathrm{NaAlH}}_{8}$, as well as a metastable compound of ${\mathrm{NaAlH}}_{7}$ under high pressures. Except for ${\mathrm{NaAlH}}_{4}$, they all containing ${\mathrm{H}}^{\ensuremath{-}}$ and ${\mathrm{H}}_{2}$ units. Electronic structure calculations reveal that ${\mathrm{NaAlH}}_{7}$ and ${\mathrm{NaAlH}}_{8}$ are metallic, while ${\mathrm{NaAlH}}_{4}$ and ${\mathrm{NaAlH}}_{6}$ are semiconductors. In addition, ${\mathrm{NaAlH}}_{8}$ exhibits a phonon anomaly (dip) in multiple phonon branches along the A-M direction. The phonon anomaly induced by Fermi-surface nesting boosts the electron-phonon coupling strength, and as a result, a superconducting transition temperature ${T}_{c}$ of 55 K was produced at 300 GPa.