Energetic stability, atomic and electronic structures of extended γ-graphyne: A density functional study

The energetic stability, atomic and electronic structures of γ-graphyne and its derivatives (γ-GYs) with extended carbon chains were investigated as a function of chain length by density functional calculations in this work. The studied γ-GYs consist of hexagon carbon rings connected by linear chains with C atoms n = 0–22. We predict that the even-numbered C chains of γ-GYs consist of alternating single and triple C-C bonds (polyyne), energetically more stable than the odd-numbered C chains made of continuous C-C double bonds (polycumulene). The calculated electronic structures indicate that γ-GYs can be either metallic (odd n) or semiconductive (even n) depending on the parity of the number of C chain atoms. The semiconducting γ-GYs are predicted to have ~1.2 eV direct band gaps and 0.1–0.2 effective electron masses independent of the chain length. Thus introducing sp carbon atoms into sp 2 -based graphene provides a novel way to open up band gaps without doping and defects while maintaining small electron masses critical to good transport properties. Graphical Abstract The typical atomic model of graphyne ( middle ) as well as their band gaps ( left ) and electron density ( right )