Non-equivalent nature of acetylenic bonds in typical square graphynes and intricate negative differential resistance characteristics.

The role of acetylenic linkage in determining the exotic band structures of 4, 12, 2- and 4, 12, 4- graphynes is reported. The Dirac bands, as confirmed by both density functional theory and tight-binding calculations, are robust and stable over a wide range of hopping parameters betweensp-sp-hybridized carbon atoms. The shifting of the crossing points of the Dirac bands along the k -path of these two square graphynes is found to be in opposite direction with the hopping along with the acetylenic bond. A real space decimation scheme has also been adopted for understanding this interesting behavior of the band structure of these two graphynes. The condition for the appearance of a nodal ring in the band structure has been explored and critically tested by appropriate Boron-Nitrogen doping. Moreover, both the graphynes exhibit negative differential resistance in their current-voltage characteristics, with 4, 12, 2- graphynes showing superiority.