Pan-C_{2(<i>n</i>+1)}: A Theoretical Prediction for 2D Carbon Allotropes

In this work, the two-dimensional (2D) periodic armchair nanoribbon (pan-C_{2(<i>n</i>+1)}) systems have been proposed and investigated by using the density functional theory (DFT). The pan-C_{2(<i>n</i>+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 3<i>n</i> rule has been revealed from their mechanical and electronic natures, which is however not entirely similar to the common 3<i>n</i> rule in the one-dimensional (1D) graphene nanoribbons. The band gaps of pan-C_{2(<i>n</i>+1)} vary in the range of 0 to 1.06 eV at the PBE0 level following the 3<i>n</i> 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-C_{2(<i>n</i>+1)} systems not only expand the carbon material family, but also provide more templates for designing functional materials through defect engineering.