Theoretical prediction of low-energy Stone-Wales graphene with an intrinsic type-III Dirac cone

Based on first principles, we predict a new low-energy Stone-Wales graphene SW40, which has an orthorhombic lattice with $Pbam$ symmetry and 40 carbon atoms in its crystalline cell forming well-arranged Stone-Wales patterns. The calculated total energy of SW40 is just about 133 meV higher than that of graphene, indicating that its excellent stability exceeds all the previously proposed graphene allotropes. We find that SW40 exhibits an intrinsic type-III Dirac cone [Phys. Rev. Lett. 120, 237403 (2018)] formed by band crossing of local linear and flat bands, which can result in highly anisotropic fermions in the system. Interestingly, such an intrinsic type-III Dirac cone can be effectively tuned by inner-layer strain and it will be transferred into type-I and type-II Dirac cones under tensile and compressed strain, respectively. Finally, a general tight-binding model was constructed to understand the electronic properties near the Fermi level in SW40. The results show that type-III Dirac cone features can be well understood by the $\pi$-electron interactions between adjacent Stone-Wales defects.

Figure 1

The optimized crystalline structures of the 30 newly discovered 2D carbons together with their names (sn-in-tn-rs) and energies (eV per atom). The nomenclature of “sn-in-tn-rs” is designed to reveal the fundamental crystal information of the space group number (sn), inequivalent atom number (in), total atom number (tn), and carbon ring sequence (rs). (Top right) The calculated total energies of all the previously predicted (red solid circles) and the newly discovered (blue solid hexagons) 2D carbon allotropes plotted as functions of the corresponding carbon densities.

Figure 2

(a) The optimized crystal structure of SW40 with well-arranged Stone-Wales defects as colored in blue and red. (b) The potential structural transition pathway from a given graphene supercell to SW40. (c) The calculated phonon band structure of SW40.

Figure 3

(a) Electronic band structures and density of states of SW40 from DFT (blue) and TB (red) calculations. (b) The 3D band structures of SW40 near the Dirac point to show its Dirac cone features. (c) The direction-dependent Fermi velocities calculated based on DFT results (white line).

Figure 4

(a) The DFT-based (blue solid lines) and TB-based (red dash lines) band structures of SW40 under selected strain ($-8\%$, $-3\%$, $-1\%$, $0\%$, $1\%$, $3\%,$ and $8\%$). (b) The direction-dependent Fermi velocities in type-II ($-8\%$), type-III ($0\%$), and type-I ($8\%$) Dirac cones and the corresponding 3D plots of the cones.