Mo$_{3}$ReRuC: A noncentrosymmetric superconductor formed in the MoReRu-Mo$_{2}$C system

A quaternary compound with the composition Mo$_{3}$ReRuC is obtained in a previously unexplored MoReRu-Mo$_{2}$C system. According to x-ray structural analysis, Mo$_{3}$ReRuC crystallizes in the noncentrosymmetric space group $P$4$_{1}$32 (cubic $\beta$-Mn type structure, $a$ = 6.8107(1) {\AA}). Below 7.7 K, Mo$_{3}$ReRuC becomes a bulk type-II superconductor with an upper critical field close to the Pauli paramagnetic limit. The specific heat data gives a large normalized jump $\Delta$$C_{\rm p}$/$\gamma$$T_{\rm c}$ = 2.3 at $T_{\rm c}$, which points to a strongly coupled superconducting state. First principles calculations show that its electronic states at the Fermi level are mainly contributed by Mo, Re and Ru atoms and strongly increased by the spin-orbit coupling. Our finding suggests that the intermediate phase between alloys and carbides may be a good place to look for $\beta$-Mn type noncentrosymmetric superconductors.