High-temperature superconductivity below 100 GPa in ternary C-based hydride MC2H8 with molecular crystal characteristics ( M = Na, K, Mg, Al, and Ga)

To explore the high-temperature superconductivity of hydrogen-rich compounds at low pressures, we have investigated the crystal structures, electronic and dynamical properties, electron-phonon interactions, and possible superconductivity of the ternary hydride $M{\mathrm{C}}_{2}{\mathrm{H}}_{8}$ ($M=$ Na, K, Mg, Al, and Ga) in the low-pressure range of $0--100\phantom{\rule{0.16em}{0ex}}\mathrm{GPa}$ based on the first-principles calculations. The results show that there is no imaginary frequency in phonon spectra for $M{\mathrm{C}}_{2}{\mathrm{H}}_{8}$ at selected pressures which indicates that $M{\mathrm{C}}_{2}{\mathrm{H}}_{8}$ is dynamically stable. Furthermore, according to the Eliashberg spectral function under pressures, $M{\mathrm{C}}_{2}{\mathrm{H}}_{8}$ is predicted to be superconducting at low pressure. Especially, the superconducting critical temperature (${T}_{c}$) of ${\mathrm{MgC}}_{2}{\mathrm{H}}_{8}$ is higher than 55 K at 40 GPa and the ${T}_{c}$ in ${\mathrm{AlC}}_{2}{\mathrm{H}}_{8}$ reaches 67 K at 80 GPa. Electronic and phonon states and the electron-phonon interactions show that H has a considerable contribution to this ternary hydride superconductor and suggest that increasing the contribution of H to total electron-phonon coupling is a way to design materials with high ${T}_{c}$. Our study shows that it is one of the feasible routes to explore the low-pressure and high-temperature superconductivity in ternary carbon-based hydrides.