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

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$^\circ$ bond-rotation in a $\sqrt{8}$$\times$$\sqrt{8}$ super-cell 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 $\sqrt{8}$ super-cell is more stable 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 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.