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A two-dimensional carbon allotrope, Stone-Wales graphene, is identified instochastic group and graph constrained searches and systematically investigatedby first-principles calculations. Stone-Wales graphene consists ofwell-arranged Stone-Wales defects, and it can be constructed through a90$^\circ$ bond-rotation in a $\sqrt{8}$$\times$$\sqrt{8}$ super-cell ofgraphene. Its calculated energy relative to graphene, +149 meV/atom, makes itmore stable than the most competitive previously suggested graphene allotropes.We find that Stone-Wales graphene based on a $\sqrt{8}$ super-cell is morestable than those based on $\sqrt{9} \times \sqrt{9}$, $\sqrt{12} \times\sqrt{12}$ and $\sqrt{13} \times \sqrt{13}$ super-cells, and is a "magic size"that can be further understood through a simple "energy splitting andinversion" model. The calculated vibrational properties and molecular dynamicsof SW-graphene confirm that it is dynamically stable. The electronic structureshows SW-graphene is a semimetal with distorted, strongly anisotropic Diraccones.

Stone-Wales graphene: A Two Dimensional Carbon Semi-Metal with Magic Stability