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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]

The presence of an extended line defect in graphene brings about some interesting electronic properties to such a truly two-dimensional (2D) carbon material, such as the energy-band engineering and valley filtering. By establishing an appropriate connection condition for the spinor wave function across the line defect, we find that the massless Dirac equation is still a valid theoretical model to describe low-energy electronic properties of the line defect embedded graphene structure. To check the validity of the wave-function connection condition, we take two kinds of line defect embedded graphene structures as examples to study the low-energy electronic states by solving the Dirac equation. First, for a line defect embedded zigzag-edged graphene nanoribbon, we obtain analytical results about the subband dispersion and eigenwave function, which coincide well with the numerical results from the tight-binding approach. Then, for a 2D graphene embedded with an extended line defect, we get an exact expression about the valley polarized electronic transmission probability, which demonstrates the simple result estimated previously in the zero-energy limit. More interestingly, our analytical result indicates that in such a 2D graphene structure a quasi-one-dimensional (ID) electronic state occurs along the line defect. And the electronic group velocity in this quasi-ID electronic state can be readily modulated by applying a strain field around the line defect. [ABSTRACT FROM AUTHOR]

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]

We present the phonon-limited electron mobility in planar T graphene and find that the mobility ∝ T − 5. 53 at low temperature T. With the increase of temperature, the power exponent 5.53 decreases towards 1. Excitingly, the room-temperature mobility of planar T graphene is 2. 78 × 1 0 6 cm 2 /Vs which is about 20.59 times as large as that of n -type graphene at the same carrier density. Different from graphene with longitudinal acoustic phonon dominating the mobility, an in-plane optical phonon mode contributes the most to the mobility of planar T graphene. • We obtain a very large room-temperature mobility (2.78 × 106 cm2/Vs) than that of monolayer graphene at the same carrier density, which makes it a promising candidate for future carbon material devices. • We observe a low-temperature behavior μ ∝ T-5.53 in the regime of partly screened electron–phonon interaction. Moreover, we predict a very high Bloch–Grüneisen temperature larger than the Debye one in planar T graphene. • Different from graphene with longitudinal acoustic phonon dominating the mobility, an in-plane optical phonon mode contributes the most to the mobility of planar T graphene. [ABSTRACT FROM AUTHOR]

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]