A two-dimensional carbon allotrope, Stone-Wales graphene, is identified in stochastic group and graph constrained searches and systematically investigated by first-principles calculations. Stone-Wales graphene consists of well-arranged Stone-Wales defects, and it can be constructed through a 90 • bond-rotation in a √ 8× √ 8 supercell of graphene. Its calculated energy relative to graphene, +149 meV/atom, makes it more stable than the most competitive previously suggested graphene allotropes We find that Stone-Wales graphene based on a √ 8 supercell is more stable than those based on √ 9 × √ 9, √ 12 × √ 12 and √ 13 × √ 13 super-cells, and is a "magic size" that can be further understood through a simple "energy splitting and inversion" model. The calculated vibrational properties and molecular dynamics of SW-graphene confirm that it is dynamically stable. The electronic structure shows SW-graphene is a semimetal with distorted, strongly anisotropic Dirac cones.
PACS numbers:Elemental carbon adopts many different allotropes, including the three-dimensional (3D) cubic diamond, hexagonal diamond and graphite, the two-dimensional (2D) graphene 1 and graphynes 2 , the one-dimensional (1D) nanotubes 3 , as well as the zero-dimensional (0D) fullerenes 4 , due to its ability to hybridize in sp, sp 2 and sp 3 . Low-dimensional carbon materials, such as graphene and nanotubes, have attracted much scientific interest in view of their novel electronic and mechanical properties 1,5,6 . In particular, graphene is a well-known Dirac-cone material that exhibits high carrier mobility 1,5,6 and the quantum Hall effect 5,7,8 due to its semi-metallicity contributed from the active π-electrons 8,9 . The successes of isolating graphene 1,10,11 from graphite have spurred many efforts in searching for other 2D carbon allotropes beyond graphene. Graphynes 12,13 are alternative ways to fill the 2D space with mixed sp-sp 2 carbon atoms. They contribute rich electronic properties, including semiconductors, semi-metals and metals. Although graphynes with sp-hybridized bonding are energetically less stable than the pure sp 2 -hybridized graphene, graphite and nanotubes, there are a few graphynes that have been experimentally synthesized 2,14 .The honeycomb-like graphene is not the only way to topologically fill 2D space with sp 2 hybridized carbon. Many other hypothetical graphene allotropes have been previously proposed. For example, the pentaheptites (R 57−1 and R 57−2 ) containing exclusively 5-7 rings proposed in 1996 15 and 2000 16,17 , the Haeckelite sheets (H 567 and O 567 ) proposed by Terrones 17 , the low-energy ψ-graphene previously proposed by Csányi 18 and recently investigated by Li 19 , the dimerites (dimerite I, II and III with metallic property) and octites (metallic octite M 1 , M 2 , M 3 and semiconducting octite SC) constructed through defects patterns 20-23 , the biphenylene sheets (New-W and New-C) containing 4-6-8 rings 24,25 , the T-graphene containing 4-8 rings 26-28 , the PO-graphene con-taining 5-8 rings (OPG-L and...
