A simple tight-binding model for typical graphyne structures.

A π-electronic tight-binding (TB) model with, at most, three independent parameters is found to well fit the density functional theory results about the dispersions of the conduction and valence bands of α-, β-, γ- and (6,6,12)-graphyne. By means of such a toy model, the electron–hole symmetry in these graphynes is demonstrated. An explicit expression of the dispersion relation of α-graphyne is obtained. The position of the Dirac point on a particular Γ–M line in the Brillouin zone of β-graphyne is analytically determined. The absence of Dirac cones in γ-graphyne is intuitively explained. Based on these interesting results, it is believed that this TB model provides a simple but effective theoretical approach for further study of the electronic and transport properties of these typical graphynes. [ABSTRACT FROM AUTHOR]