In this work, the two-dimensional (2D) periodic armchair nanoribbon (pan-C2(n+1)) systems have been proposed and investigated by using the density functional theory (DFT). The pan-C2(n+1) systems can be easily obtained by in-plane rotating the carbon pairs C2 at certain positions in the monolayer graphene (G). The graphene nanoribbon patterns are connected by the resulting line defects composed of the 5- and 8-membered rings without edge and dangling bond. Their structural stabilities, mechanical strengths, and electronic features have been systematically discussed. A 3n rule has been revealed from their mechanical and electronic natures, which is however not entirely similar to the common 3n rule in the one-dimensional (1D) graphene nanoribbons. The band gaps of pan-C2(n+1) vary in the range of 0 to 1.06 eV at the PBE0 level following the 3n rule. This tunable semiconducting property offers the probabilities of designing 2D logic circuits on the scale of single atomic thickness, gas sensors, and so on. Moreover, these pan-C2(n+1) systems not only expand the carbon material family, but also provide more templates for designing functional materials through defect engineering.

Defects, Electrical conductivity, Energy, Monolayers, Two dimensional materials