Topological hybrid nodal-loop semimetal in a carbon allotrope constructed by interconnected Riemann surfaces

Abstract

We predict by ab initio calculations an $\mathrm{all}\ensuremath{-}s{p}^{2}$ nanostructured carbon phase of a topological hybrid nodal-loop semimetal with momentum-dependent crossings of linear bands near the Fermi level. This carbon phase is assembled from interconnected Riemann surfaces, naturally occurring as screw dislocations in graphitic carbons, which not only result in notably higher stability than most previously reported allotropes but also sustain a strain-robust nodal loop up to 75% elastic stretch due to mirror symmetry. The design strategy, based on the elegant topology of Riemann surfaces, can yield a family of topological carbon materials with fascinating mechanical and electronic properties.