Electronic band structure of carbon honeycombs

In this article, we present the electronic properties of various carbon honeycombs (C-honeycombs) with different cell sizes and junction types based on ab initio calculations. Among the three typical C-honeycombs with junctions connected via the zigzag edge, the armchair edge, or the hybrid edges of graphene nanoribbons, it is found that the zigzag C-honeycombs and the hybrid ones exhibit metallic properties. However, the armchair C-honeycombs are metallic only if the number of atomic planes N of the graphene nanoribbon in the C-honeycomb sidewall follows N = 3p+1, with p as an integer and are semiconducting for other N. For those semiconducting ones, the bandgap of the C-honeycomb is about 1.19 eV with the narrowest sidewall (5.2 Å) and monotonically decreases to about 0.15 eV when the width is increased to 34.8 Å. The semiconducting nature of such C-honeycombs with nanometer size pores may be used for lightweight semiconductor in electronic devices or supercapacitor energy storage. As a comparison, we show that all boron honeycombs are metallic, and their electronic properties are independent of sidewall widths.