Non-equivalent nature of acetylenic bonds in typical square graphynesand 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 between sp - 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 BN doping. Moreover, both the graphynes exhibit negative differential resistance in their
current-voltage characteristics, with 4,12,2- graphynes showing superiority.