Superconductivity of carbon compounds with sodalite structure

On the basis of first-principles calculations, we propose a superconductivity of carbon compounds with a sodalite structure, which is similar to a hydrogen compound with a very high superconducting transition temperature, $T_{rm c}$. Our systematic calculation shows that some of these carbon compounds have a $T_{rm c}$ of up to about 100 K at a pressure of about 30 GPa, which is lower than that of superconducting hydrides (above 100 GPa). The obtained phonon dispersions appear to be similar to each other, and this suggests that the sodalite structure may be a key to generating phonon-mediated high-$T_{rm c}$ superconductivity.