A family of all sp²-bonded carbon allotropes of topological semimetals with strain-robust nodal-lines

We report on a family of all-sp² carbon allotropes constructed by interconnected screw dislocations with complementary chiralities through atomistic calculations. The carbon allotropes have lattice periodicities defined by the interspacing among screw dislocations and are shown to withstand an elastic stretch of over 90% along the direction of the dislocation axis. A subset of these allotropes exhibit interesting unclosed, topological nodal-lines near the Fermi level, while the other subset with a higher symmetry are topological semimetals with a nodal-loop at the Fermi level. Moreover, the topological semimetallicity in these allotropes is robust to an elastic stretch of up to 75% due to their unique symmetry, in contrast to a common view that a tensile strain tunes a topological material into a trivial semiconductor. Of relevance is that these allotropes are notably more stable than most of previously reported allotropes and likely to exist in specimens of detonation soot according to simulated X-ray diffraction patterns, suggesting the possibility of their experimental realizations.