A theoretical study of the smallest tetrahedral carbon schwarzites

We present a tight-binding molecular-dynamics investigation on the structural, elastic and electronic properties of the smallest periodic tetrahedral carbon schwarzites fcc-$\rm (C_{28})_2$, fcc-$\rm (C_{36})_2$ and fcc-$\rm (C_{40})_2$. Although their unit cells are equivalent to the fullerenes $\rm C_{20}$, $\rm C_{28}$ and $\rm C_{32}$, respectively, their stability is found to be much higher. Moreover they present alternatively metallic or insulating character, which would make this class of hypothetical materials suitable to a wide range of applications