An Ab Initio Investigation of Energy Bandgap of Monolayer and Bilayer Graphene Nanoribbon Based on Different Basis Sets

We investigated the electronic structure of monolayer and bilayer graphene nanoribbon with armchair edges (AGNR_M and AGNR_B respectively) based on density functional theory using single-zeta (SZ) and double -zeta (polarized) (DZP) basis sets. We first optimize the atomic structure of an AGNR_B and found that DZP is better suited to account for the interlayer interaction. Next we calculate the energy band diagram of the AGNR_M and AGNR_B of different width, and study dependence of the band gap (E_g) on the widths. Like AGNR_M, AGNR_B also shows three different groups in terms of energy bandgap vs. width. In general, AGNR_B is found to have a lower E_g than AGNR_M. Especially for N=3p+2 family, while it is semiconducting for AGNR_M, the E_g of AGNR_B is very small and can be considered as metallic at room temperature. Furthermore, we investigate the relationship between E_g and the interlayer distance (D) of AGNR_B. From our calculation, E_g is found to be strongly influenced by D and E_g increases as D increases. Finally, comparing solely on E_g, we can see that both SZ and DZP calculations provide information on the three trends of the AGNR_M and AGNR_B, with small differences in the absolute values and hence it may be possible to use SZ for rapid preliminary investigation of the electronic properties of AGNR systems.