The Band-Gap Modulation of Graphyne Nanoribbons by Edge Quantum Entrapment

Using ab initio calculation coupled with the bond-order-length-strength (BOLS) approximation, we investigate the configurations and electronic properties of (α, β)-graphyne nanoribbons (GYNRs) with armchair (AGYNRs) and zigzag (ZGYNRs) edges. Our investigation shows that the armchair-edged β-GYNRs and all α-GYNRs are semiconductors with suitable band-gaps, and that their band-gaps increase as the widths of nanoribbons decrease; on the other hand, zigzag-edged β-GYNRs appear to be zero-band-gap materials. Observation results suggest that (i) atomic undercoordination shortens and stiffens the C–C bond, which contributes to the Hamiltonian and hence widens the band-gap intrinsically; (ii) zigzag-edged β-GYNRs lack a band-gap due to the edge-undercoordinated atoms lacking the energy to open the β-graphyne gap; and (iii) the edge-undercoordination of atoms occurs during charge entrapment.