Three-Dimensional Crystalline Modification of Graphene in all-sp2 Hexagonal Lattices with or without Topological Nodal Lines.

The discovery of fullerenes, nanotubes, and graphene has ignited tremendous interest in exploring additional all-sp2 carbon networks with novel properties. Here we identify by ab initio calculations a new series of three-dimensional crystalline modification of carbon in all-sp2 bonding networks that comprise trigonal polycyclic benzenoid nanoflakes in a 2 n2 ( n ≥ 4) atom hexagonal cell. The resulting 32-, 50-, 72-, and 98-atom structures (termed as tr32, tr50, tr72, and tr98) in trigonal ( P3̅ m1) symmetry are characterized as the crystalline modification of ( n × n × 1)-graphene in AA stacking, which are energetically more stable than or comparable to the solid fcc-C60 and (5,5) carbon nanotube. Electronic band structure calculations show that tr72 without 2 d (1/3, 2/3, z) symmetric carbon atoms is a semiconductor, while tr32, tr50, and tr98 with 2 d carbon atoms are topological nodal-line semimetals comprising nodal lines on the H-K-H' edge in the hexagonal Brillouin zone, as a three-dimensional extension of the Dirac point at the K-point in two-dimensional graphene. The present findings establish an additional crystalline modification of graphene in the all-sp2 carbon allotrope family and offer insights into its outstanding structural and electronic properties.