Pentagraphite C8 : An all- sp2 topological nodal-line semimetal

Recent research predicted stable two-dimensional pentagraphene in $s{p}^{2}\text{\ensuremath{-}}s{p}^{3}$ bonding states and three-dimensional pentadiamond (BC14) in all-$s{p}^{3}$ bonding states, both comprising five-membered carbon-ring networks and exhibiting semiconducting character with sizable electronic band gaps. Here we identify by ab initio calculations an all-$s{p}^{2}$ carbon allotrope, also comprising the unusual five-membered rings as the basic structural units, with an eight-atom monoclinic primitive cell in $C2/m$ (${C}_{2h}^{3}$) symmetry, termed mpg-${\mathrm{C}}_{8}$ pentagraphite. Total-energy calculations show that mpg-${\mathrm{C}}_{8}$ is more stable than or comparable to the previously reported all-$s{p}^{2}$ rh6 polybenzene and all-$s{p}^{3}$ BC14 pentadiamond. Electronic band calculations reveal that mpg-${\mathrm{C}}_{8}$ is a topological nodal-line semimetal protected by the inversion ($P$) and time reversal ($T$) symmetry, comprising two nodal rings centered at the $\mathrm{\ensuremath{\Gamma}}$ and $M$ points in the bulk first Brillouin zone and one projected surface flat band around the Fermi level on its (010) surface. These results establish a distinct type of carbon phase with nontrivial topological properties and offer insights into its outstanding electronic properties.