Stone-Wales graphene: A two-dimensional carbon semimetal 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 $\sqrt{8}\times \sqrt{8}$ 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 (SW-graphene) based on a $\sqrt{8}$ supercell is more stable than those based on $\sqrt{9}\times \sqrt{9},\sqrt{12}\times \sqrt{12}$, and $\sqrt{13}\times \sqrt{13}$ supercells, 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.

Figure 1

Calculated energies (relative to graphene) and carbon densities of the new discovered (blue hexagon) and previously proposed (red balls) graphene allotropes with energy relative to graphene less than 550 meV per atom. Inset: The crystalline view of the most stable one (SW graphene) with symmetry of $Cmmm$, showing its topological pattern containing five-, six-, and sevenfold carbon rings.

Figure 2

The first Brillouin zone (BZ) (a), the band structures (b), the 2D color mapping of the energy differences between LCB and HVB (c), as well as the band decomposed charge density distributions of SW-graphene (d).

Figure 3

The 3D plot of the Dirac cone formed by the highest valence band (HVB) and the lowest conduction band (LCB) in the vicinity of the Dirac point ($D_6$) and the corresponding direction-dependent Fermi velocities for Fermions in SW-graphene.

Figure 4

Relative energies (a) and SWD rotation energies ($E_{\sqrt{N}}-N{E}_{\text{graphene}}$) (b) of $\sqrt{N}\times \sqrt{N}$ graphene supercells with a single SWD. SW-graphene corresponds to $N=8$. Red balls denote structures that adopt $Cmmm$ symmetry; blue hexagons denote structures adopting $P2/m$ symmetry.

Figure 5

Energy splitting and inversion model (left: rotation energies eV per cell; right: relative energies eV/atom relative to graphene) based on the comparison of energy changes between $\sqrt{7},\sqrt{8}-Cmmm,\sqrt{8}-P2/m,\sqrt{9},\sqrt{12}$, and $\sqrt{13}$ in three steps after bond rotation, namely, electronic minimization in fixed configuration (electron), ionic relaxation (ion), as well as full lattice and ionic relaxation (lattice).