Topological semimetal in an sp2−sp3 hybridized carbon network with nodal rings

Abstract

There have been several proposals that three-dimensional allotropes of carbon formed by graphene networks can support two types of topological nodal line semimetals: type A has closed nodal rings inside the first Brillouin zone (BZ), and type B has nodal lines traversing the whole BZ to be periodically connected. Among these proposals, it has been found that nearly all-$s{p}^{2}$ hybridized allotropes tend to hold A-type closed nodal rings, while the $s{p}^{2}\text{\ensuremath{-}}s{p}^{3}$ hybridized allotropes tend to hold B-type periodic nodal lines. Here we identify by ab initio calculations an $s{p}^{2}\text{\ensuremath{-}}s{p}^{3}$ hybridized carbon allotrope in $Pcca$ (${D}_{2h}^{8}$) symmetry as a topological nodal line semimetal with two A-type closed nodal rings on the ${k}_{y}=0$ and ${k}_{y}=\ensuremath{\pi}$ mirror planes, respectively. The projections of these two nodal rings onto (010) surfaces form concentric ellipses with different size. The drumhead surface states appear in the region enclosed by the bigger ring but disappear inside of the smaller ring. This is consistent with the distribution of the Berry phase calculated along the [010] periodic reciprocal lattice. An effective $k\ifmmode\cdot\else\textperiodcentered\fi{}p$ model has been proposed, and the parameters have been obtained through fitting the ab initio results. The model can reproduce the nodal rings in the shape of an ellipse, satisfying the twofold rotational symmetry. Meanwhile, the simulated x-ray diffraction spectrum matches well with the recently reported distinct diffraction peaks found in the diamond-rich coatings on stainless steel substrate. These results establish a carbon phase with intriguing structural and electronic properties and expand our understandings about topological nodal lines in carbon networks.