Topological nodal line semimetal with large nodal ring in an all- sp2 hybridized carbon network formed by all-ten-membered carbon rings

Carbon can form versatile allotropes due to its multiple bonding connections and the prediction of new carbon structures and properties has long been a hot topic. In 1983, Hoffmann et al. [J. Am. Chem. Soc. 105, 4831 (1983)] have reported an all-$s{p}^{2}$ hybridized carbon allotrope with a 16-atom body-centered-tetragonal unit cell in $\mathrm{I}{4}_{1}/\mathrm{amd}$ (${D}_{4h}^{19}$) symmetry, which is dubbed as cT16 carbon in this work. Here we report by ab initio calculations a systematical study on the structural, energetic, dynamical, and electronic properties of cT16 carbon. Interestingly, cT16 carbon is linked with all-ten-membered carbon rings. The phonon band spectrum calculations confirm its dynamical stability and ab initio molecular dynamics simulations prove its thermal stability up to 900 K. Previously cT16 carbon was widely considered as a simple metallic carbon. However, our detailed electronic band structures calculations reveal that cT16 is actually a topological nodal line semimetal with a large closed nodal ring centering the high-symmetric $\mathrm{\ensuremath{\Gamma}}$ point. It nearly encloses the entire ${k}_{z}=0$ mirror plane, thus the drumheadlike surface bands can nearly cover the entire projected ($11\overline{1}$) surface Brillouin zone, which makes cT16 carbon an ideal nodal line semimetal. The simulated x-ray diffraction pattern of cT16 carbon matches well with one of the previously unexplained experimental peaks found in the diamond rich coatings grown on the stainless steel substrate. Our findings have provided insight for this well-known cT16 carbon, enriched the family of carbon allotropes with exotic topological electronic properties, suggested a viable route for its synthesis, and also provided an reasonable explanation for previous experimental data.