Hybrid nodal chain in an orthorhombic graphene network

Abstract

A topological nodal line (NL) semimetal is a kind of special three-dimensional semimetal state with only nodal lines around the Fermi level. It has been revealed that there are basically two types of NLs when spin-orbit coupling is not considered for electronic system: One is dubbed $s$-NLs, protected by a combinational symmetry $S$ of spatial inversion $(P)$ and time reversal $(T)$, i.e., $S=PT$; the other one is $m$-NLs, protected by mirror $(M)$ or glide symmetry, constraining the NL inside certain symmetrical planes. However, a hybrid nodal chain (HNC), composed of linked $s$-NLs and $m$-NLs from the same two crossing bands, has not been well studied so far. Here, we identify by ab initio calculations a new all-$s{p}^{2}$ hybridized carbon allotrope as a good candidate, which has a unit cell of 24 carbon atoms with $Pnna$ $({D}_{2h}^{6})$ symmetry and is termed $\mathrm{oP}\text{\ensuremath{-}}{\mathrm{C}}_{24}$ carbon. The HNC hosted by $\mathrm{oP}\text{\ensuremath{-}}{\mathrm{C}}_{24}$ can be simply described by a two-band $\mathbit{k}\ifmmode\cdot\else\textperiodcentered\fi{}\mathbit{p}$ model, distinguished from the three-band model proposed for another HNC candidate in the TiRhAs family. This kind of HNC is proposed in a real material here and paves the way for further theoretical and experimental investigations.