Superconductivity of Carbon Compounds with Sodalite Structure

We investigate the superconductivity of carbon compounds with a sodalite structure, which are similar to hydrogen compounds showing the high-temperature superconductivity. A systematic analysis by first-principles calculations is carried out, including examination of mechanical and dynamic instabilities under external pressure $P$. These instabilities are classified on the phase diagram for the effective doping charge versus the lattice constant of the system. We also present the superconducting transition temperature $T_{\mathrm{c}}$ as a function of $P$ for many carbon compounds and a pure carbon system with the sodalite structure. Some of them have $T_{\mathrm{c}}$ of up to about 100 K at $P>\sim 30$ GPa, and the results suggest that the sodalite structure of carbon may be a key to producing phonon-mediated high-$T_{\mathrm{c}}$ superconductivity.