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Graphene has intrinsic edge states localized at zigzag edge or lattice defect. Helical boundary states can also be established in such a two-dimensional carbon material at the boundary of topological insulator (TI) phase realized by the extrinsic Rashba spin–orbital coupling (SOC) in gated bilayer graphene. We theoretically investigate the interaction between these two kinds of edge (boundary) states when they coexist in a bilayer graphene. We find that this interaction gives rise to some very interesting results. In a zigzag edged nanoribbon of bilayer graphene, it is possible that the TI helical state does not localize at the TI phase boundary. Instead it moves to the nanoribbon edge even though the SOC is absent therein. In a bulk lattice of bilayer graphene embedded with two line defects, the numbers of helical state subbands at the two line defects are not equal to each other. In such a case, the backscattering lacking is still forbidden since the Kramers pairs are valley polarized. [ABSTRACT FROM AUTHOR]

Abstract: It was recently reported that a kind of graphene line defect can be fabricated in a controllable experimental way. In the present work we theoretically investigate the band structure and the electronic transport properties of a graphene superlattice formed by embedding periodically line defects in the graphene lattice. Based on the calculated results, we suggest that such a superlattice can be used as a quantum wire array which can carry much larger current than a single graphene nanoribbon. A remarkable advantage of this superlattice over other quantum wires is that the electronic transport in it is insensitive to scattering effects except that the scattering potential range is smaller than the graphene lattice constant. Moreover, we find that the anisotropy of the Dirac cone presented in this superlattice has a nontrivial influence on the universal minimal conductivity and the sub-Poissonian shot noise of graphene. [Copyright &y& Elsevier]

Abstract: We develop a tight-binding theory to study the electronic transport through an extended line defect in monolayer graphene. After establishing an analytical expression of the transmission probability, we clarify the following issues concerning the valley polarization in the electronic transport process. Firstly, we find that the valley polarization is robust in the total linear dispersion region. More interestingly, we find that the lattice deformation around the line defect play an important role in tuning the incident angle for complete transmission. Finally, we indicate that next nearest neighbor interaction only causes a small suppression to the valley polarization. [Copyright &y& Elsevier]

Abstract: Optical conductivity of a graphene sheet subject to a one-dimensional cosinusoidal potential is studied. We find that the optical conductivity can be tuned by the strength of the superlattice potential. When this strength is within a certain range the terahertz conductivity can be enhanced by two orders of magnitude. [ABSTRACT FROM AUTHOR]