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We present and discuss practical techniques for formulating effective models to describe the low-energy electronic properties of bilayer graphene systems. We show that such effective models are constructed from a collection of appropriate single-layer Bloch states of two graphene layers. In general, the obtained effective models allow the construction of a so-called moiré band structure. However, it is not the result of an irreducible representation of a translation symmetry group of the bilayer lattices except for the commensurate bilayer configurations. We also point out that the commensurate bilayer configurations are classified into three categories depending on the divisibility of the difference between two commensurate integer indices by 3. The electronic band structure of three lattice configurations, one for each category, is shown. Especially by combining with a real-space calculation, we validate the working ability of constructed effective models for generic bilayer graphene systems by showing that the effects of interlayer sliding are diminished by twisting. This result is consistent with the invariance of effective models under the interlayer sliding operation.

Dirac points are found to emerge due to the crossing of bands in the electronic structure of so-called sliding bilayer graphene. Group representation theory analysis corroborated with a tight-binding model for the ${p}_{z}$ orbitals is employed to demonstrate that the band crossings of energy dispersion curves at generic $\mathbf{k}$ points are guaranteed by the compatibility relations between the symmetries of eigenstates at the high-symmetry $\mathbf{k}$ points in the Brillouin zone. The Lifshitz transition picture and the transport properties of the systems are shown as consequences of the presence of Dirac points in governing the geometrical and topological properties of the Fermi energy surfaces.

The operation and performance of top-gated sub-100 nanometer graphene channel field-effect transistors were investigated. The device model is designed for graphene with a narrow energy band gap epitaxially grown on the SiC substrate. The issue of graphene-metallic lead coupling is appropriately taken into account. By assuming the graphene-metal physisorption contact, a self-consistent calculation reproduces two regions of high carrier density at the ends of the graphene channels underneath the metallic leads according to the charge transferred effect between the metallic lead surface and graphene. The charge carrier densities in these source and drain regions, however, are not pinned, but vary with respect to the drain and gate voltages. It is shown that, in general, the graphene channel supports the ambipolar characteristics for all device samples, but for the samples with the channels shorter than 40 nm, the current-voltage characteristic takes the exponential law. Particularly, the current saturation with a rather small output conductance of 126 S/m was observed in a sufficiently large range of drain voltage due to the dominance of the thermionic emission and conventional tunneling mechanisms to the band-to-band tunneling. A rough assessment of the device performance was also carried out. It reveals an extremely high cutoff frequency in the order of $$10^3\hbox { GHz}$$ and a linear scaling rule for transistors with the channel length longer than 40 nm. The behaviour and magnitude of these quantities are consistent with an experimental study of sub-100 nm devices fabricated using the self-alignment technique.

Understanding the mechanisms governing the optical activity of layered-stacked materials is crucial to the design of devices aimed at manipulating light at the nanoscale. Here, we show that both twisted and slid bilayer graphene are chiral systems that can deflect the polarization of linear polarized light. However, only twisted bilayer graphene supports circular dichroism. Our calculation scheme, which is based on the time-dependent Schr\"odinger equation, is particularly efficient for calculating the optical-conductivity tensor. Specifically, it allows us to show the chirality of hybridized states as the handedness-dependent bending of the trajectory of kicked Gaussian wave packets in bilayer lattices. We show that nonzero Hall conductivity is the result of the noncanceling manifestation of hybridized states in chiral lattices. We also demonstrate the continuous dependence of the conductivity tensor on the twist angle and the sliding vector., Comment: 24 pages, 6 figures

We report on C-doped ZnO, with different weight percentages of dopant, prepared by a high-energy ball milling method. The annealing conditions with temperature of 800 °C and in argon environment appear to be the optimal conditions for producing good quality crystals as well as pure UV emission. XRD and FTIR analysis indicate the substitution of C for Zn. In addition, Raman spectroscopy suggests a disordered graphitic layer covering the crystals. Photoluminescence investigation reveals the continuous quenching of visible region upon increasing C concentration and the intensity ratio between defect-related and UV emission can be as negligible as 0.02. The passivation of surface defects and the creation of a non-radiative recombination pathway by carbon integration are proposed as possible origins of the suppression.

We characterise the dynamics of electrons in twisted bilayer graphene by analysing the time-evolution of electron waves in the atomic lattice. We perform simulations based on a kernel polynomial technique using Chebyshev polynomial; this method does not requires any diagonalisation of the system Hamiltonian. Our simulations reveal that the inter-layer electronic coupling induces the exchange of waves between the two graphene layers. This wave transfer manifests as oscillations of the layer-integrated probability densities as a function of time. For the bilayer case, it also causes a difference in the wavefront dynamics compared to monolayer graphene. The intra-layer spreading of electron waves is irregular and progresses as a two-stage process. The first one characterised by a well-defined wavefront occurs in a short time | a wavefront forms instead during the second stage. The wavefront takes a hexagon-like shape with the vertices developing faster than the edges. Though the detail spreading form of waves depends on initial states, we observe localisation of waves in specific regions of the moir\'e zone. To characterise the electron dynamics, we also analyse the time auto-correlation functions. We show that these quantities shall exhibit the beating modulation when reducing the interlayer coupling., Comment: 14 pages, 11 figures

We investigate the electronic and optical properties of twisted bilayer graphene with arbitrary twist angles $\ensuremath{\theta}$. Our results are based on a method of evolving in time quantum states in lattice space. We propose an efficient scheme of sampling lattice nodes that helps to reduce significantly computational cost, particularly for tiny twist angles. We demonstrate the continuous variation of the density of states and the optical conductivity with respect to the twist angle. It indicates that the commensurability between the two graphene layers does not play an essential role in governing the electronic and optical properties. We point out that, for the twist angles roughly in the range $0.{1}^{\ensuremath{\circ}}l\ensuremath{\theta}l{3}^{\ensuremath{\circ}}$, the density of states in the vicinity of the Fermi energy exhibits the typical W shape with a small peak locating at the Fermi energy. This peak is formed as the merging of two van Hove peaks and reflects the appearance of states strongly localized in the AA-like region of moir\'e zones. When decreasing the twist angle to zero, the W shape is gradually transformed to the U shape, which is seen as the behavior of the density of states in the limit of $\ensuremath{\theta}\ensuremath{\rightarrow}{0}^{\ensuremath{\circ}}$.

Using an empirical atomistic approach associated with the method of random-phase approximation, we investigated the behaviors of plasmons in heavily doped graphene. We show that, in the range of low energy and of long wavelength, a novel plasmon mode may appear below the conventional Dirac plasmon. The novel mode is strongly anisotropic and only appears in a finite range of the transfer wave number. It is found that the appearance of the novel plasmon stems from the anisotropy of the energy surfaces forming the Dirac cones and the inequivalance of the two Dirac valleys in the Brillouin zone. Interestingly, we demonstrate that these two unique electronic features of graphene act, respectively, as the necessary and sufficient factors in governing the formation of the novel plasmon mode.

We propose a computational approach to combining the plane-wave method and the real-space treatment to describe the periodic variation in the material plane and the decay of wave functions from the material surfaces. The proposed approach is natural for two-dimensional material systems and thus may circumvent some intrinsic limitations involving the artificial replication of material layers in traditional supercell methods. In particular, we show that the proposed method is easy to implement and, especially, computationally effective since low-cost computational algorithms, such as iterative and recursive techniques, can be used to treat matrices with block tridiagonal structure. Using this approach we show first-principles features that supplement the current knowledge of some fundamental issues in bilayer graphene systems, including the coupling between the two graphene layers, the preservation of the $\ensuremath{\sigma}$ band of monolayer graphene in the electronic structure of the bilayer system, and the differences in low-energy band structure between the AA- and AB-stacked configurations.

A numerical scheme based on the tight-binding description for pz-electrons in graphene was developed to study the formation and behaviors of plasmons in this two-dimensional electron system. The random phase approximation has been used to calculate the dielectric function for arbitrary temperature and doping level. We show that at zero-doping, only one kind of plasmons of long wavelength is observed at sufficiently high temperature. At finite doping, such plasmons exist even at zero temperature, but strongly damped, due to the interplay between the intra- and inter-band transition processes. Particularly, we show a significant dependence of the plasmon spectrum on the wave-vector direction in the regime of high doping, which is the reflection of the anisotropy of the energy surfaces far from the Dirac point.

The non-equilibrium Green function (NEGF) technique is used to solve the quantum transport equation in resonant tunneling diodes (RTDs). The charge interaction is treated self-consistently to include rigorously the space-charges effects. Reasonable results for the potential profile, the transmission probability, and the current-voltage characteristics have been obtained. The effect of temperature on the current-voltage (I-V) characteristics is investigated. Particularly, the current noise spectral density has been extracted following both coherent and sequential tunneling approaches. Our conclusion of the dominance of the coherent and sequential tunneling according to the transport regime is consistent with recent theoretical analyses and experimental data.

In this work, the optical responses of graphene superlattices, i.e. graphene subjected to a periodic scalar potential, are theoretically reported. The optical properties were studied by investigating the optical conductivity, which was calculated using the Kubo formalism. It was found that the optical conductivity becomes dependent on the photon polarization and is suppressed in the photon energy range of (0, Ub), where Ub is the potential barrier height. In the higher photon energy range, i.e. Ω > Ub, the optical conductivity is, however, almost identical to that of pristine graphene. Such behaviors of the optical conductivity are explained microscopically through the analysis of the elements of optical matrices and effectively through a simple model, which is based on the Pauli blocking mechanism.

High crystalline quality ZnS nanowires were fabricated using the thermal evaporation method. They were then oxidized in air at different temperatures to form a one-dimensional protuberant ZnO/ZnS structure. It was argued that the oxidation at low enough temperature can significantly improve the quality of the ZnS nanowires by passivating dangling bonds on the nanowire surface as the absorption of oxygen atoms. This study provides a simple approach for synthesizing optically active ZnO/ZnS heterostructures.

An atomistic Green's function approach to simulating electron and phonon transport in graphene nanoribbons (GNRs) is presented. Phonons are described by an empirical Force-Constant model including interactions up to the fifth nearest neighbour while the nearest neighbour tight-binding Hamiltonian is used for electrons. The model was applied to investigate the edge dependence of GNR thermoelectric properties. The factor of merit ZT appears to be strongly enhanced in mixed-edge ribbons.

We propose an extension of the Landauer-Buttiker scattering theory to include effects of interaction in the active region of a mesoscopic conductor structure. The current expression obtained coincides with those derived by different methods. A new general expression for the noise is also established. These expressions are then discussed in the case of strongly sequential tunneling through a double-barrier resonant tunneling structure., 11 pages, 2 figures, rediscussion

We show that periodic scalar potentials can induce the localization of some electronic states in graphene. Particularly, localized states are found at energies outside the potential variation range and embedded in the continuum spectrum of delocalized ones. The picture of the connection of wave functions with typical symmetries defined in relevant-edge nanoribbons is employed to explain the formation of the electronic structure and to characterize/classify eigen-states in graphene superlattices.

A physical model is proposed to clarify the electron transport through graphene-metal interfaces. It is based on an effective description of the coupling between the graphene π-bands and the metal sd- and d-bands. Applying this model to vertically symmetrical metal-graphene-metal structures, we show that the current-voltage characteristics can be either linear or non-linear with a negative or positive differential resistance depending on the dominance of the d-like or s-like electrons in the metal as well as the graphene-metal coupling.

We investigate the transport properties of p+/p junctions based on zigzag-edge graphene strips by means of numerical quantum simulation. The p+ and p domains are created by field effect using appropriate gate electrodes. A negative differential resistance behavior is predicted regardless of the evenness/oddness of the zigzag line number of the ribbon with peak-to-valley current ratio reaching the value of 10 at room temperature. Besides the role of the parity selective rule, the phenomenon is explained as resulting from the suppression of the coherent transition due to the mismatch of modes in the left and right sides of the junction. The influence of various factors governing the peak-to-valley current ratio is analyzed. In particular, it is found that the negative differential resistance may be severely affected by the roughness of ribbon edges.

We analyze the spin-dependent transport in single ferromagnetic gate structures based on armchair graphene nanoribbon (GNR) using the non-equilibrium Green's function method in a tight binding model. It is shown that the spin polarized current oscillates as a function of the gate-induced barrier height. For perfect GNRs, the larger the energy band gap, the stronger the oscillation of the spin polarization. However, though the edge roughness of the ribbons tends to enlarge the band gap, it also strongly reduces the conductance which finally degrades the spin polarized current.

Using the non-equilibrium Green's functions formalism in a tight binding model, the spin-dependent transport in armchair graphene nanoribbon (GNR) structures controlled by a ferromagnetic gate is investigated. Beyond the oscillatory behavior of conductance and spin polarization with respect to the barrier height, which can be tuned by the gate voltage, we especially analyze the effect of width-dependent band gap and the nature of contacts. The oscillation of spin polarization in the GNRs with a large band gap is strong in comparison with 2D-graphene structures. Very high spin polarization (close to 100%) is observed in normal-conductor/graphene/normal-conductor junctions. Moreover, we find that the difference of electronic structure between normal conductor and graphene generates confined states in the device which have a strong influence on the transport quantities. It suggests that the device should be carefully designed to obtain high controllability of spin current., Comment: 8 pages, 7 figures

Motivated by recent studies on the use of graphene for new concepts of electronic/spintronic devices, the authors develop an efficient calculation method based on the nonequilibrium Green’s function to solve the quantum relativisticlike Dirac’s equation that governs the low-energy excited states in graphene. The approach is then applied to investigate the electronic transport and the spin polarization in a single-graphene barrier structure. The obtained results are presented and analyzed in detail aiming to highlight typical properties of the considered graphene structure as well as the efficiency of the developed approach that both may be helpful for further development in electronic devices and in spintronics.

Using the nonequilibrium Green’s function formalism, the authors investigate the effect of the electron-phonon interaction on the current and shot noise in one dimensional resonant tunneling structures. Besides the well-known current behavior, they particularly show that the shot noise may be enhanced over the Poissonian value due to the phonon-assisted tunneling effect. The observed super-Poissonian noise is then interpreted as a result of the competition between the coherent and sequential current components.

Using the nonequilibrium Green’s function method, gate current characteristics are investigated for nanometer-scaled double-gate metal-oxide-semiconductor field-effect transistor. The mode-space approximation is, at the first stage of the calculation, used to obtain self-consistently the potential profile and the charge distribution in the structure. This solution is then used to solve the two-dimensional transport equation to extract the desired quantities. In addition to the dependence of the gate-leakage current on the gate bias and on the oxide thickness, our calculation shows the oscillation behavior of the leakage current versus the drain voltage. It is explained as the result of the strong quantization of electronic states inside the device, giving a resonant-like character to the tunneling of charges from source and drain contacts to the gates. This effect is strongly dependent on the gate length.