Electronic Structure of Large-Scale Graphene Nanoflakes

With the help of the recently developed SIESTA-PEXSI method [J. Phys.: Condens. Matter \textbf{26}, 305503 (2014)], we perform Kohn-Sham density functional theory (DFT) calculations to study the stability and electronic structure of hexagonal graphene nanoflakes (GNFs) with up to 11,700 atoms. We find the electronic properties of GNFs, including their cohesive energy, HOMO-LUMO energy gap, edge states and aromaticity, depend sensitively on the type of edges (ACGNFs and ZZGNFs), size and the number of electrons. We observe that, due to the edge-induced strain effect in ACGNFs, large-scale ACGNFs' cohesive energy decreases as their size increases. This trend does not hold for ZZGNFs due to the presence of many edge states in ZZGNFs. We find that the energy gaps $E_g$ of GNFs all decay with respect to $1/L$, where $L$ is the size of the GNF, in a linear fashion. But as their size increases, ZZGNFs exhibit more localized edge states. We believe the presence of these states makes their gap decrease more rapidly. In particular, when $L$ is larger than 6.40 $nm$, we find that ZZGNFs exhibit metallic characteristics. Furthermore, we find that the aromatic structures of GNFs appear to depend only on whether the system has $4N$ or $4N+2$ electrons, where $N$ is an integer.