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 -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.

No abstract

No abstract

We theoretically demonstrate that a kind of extended line defect, an experimentally available topological defect in graphene lattice, can induce one-dimensional boundary states. And in the presence of the pseudomagnetic field generated by an inhomogeneous strain, such boundary states are valley chiral in the sense of electronic propagation direction being locked to its valley degree of freedom. Based on such an electronic characteristic, we further show that when the line defect is embedded in the strained graphene strip, the valley filtering and valley valve functions can be realized in the electronic transport process. Therefore, we argue that the line defect can play a key role in the field of graphene valleytronics, instead of a zigzag-edged graphene nanoribbon.

Within the continuum model, i.e., the Dirac equation approach, we study the boundary states around the line defect in graphene in the quantum Hall regime. We find that the boundary states localize at the opposite sides of the line defect if they propagate toward the opposite directions. Meanwhile, some boundary states show simultaneously the valley and sublattice polarizations. In addition, a pseudomagnetic field induced by an inhomogeneous strain field, in place of the real magnetic field, can drive the line defect embedded graphene to the quantum valley Hall regime, due to the occurrence of the valley polarized boundary states.