Abstract:
The electronic excitations of bilayer graphene (BLG) under a magnetic field are investigated with the use of the Peierls tight-binding model in conjunction with random-phase approximation (RPA). The interlayer atomic interactions, interlayer Coulomb interactions, and magnetic field effects are simultaneously included in the dielectric-function matrix. That enables us to derive the magneto-Coulomb-excitation spectrum of different stacking structures. The two typical arrangements of BLGs, AB and AA, are considered in this article. AB-BLG exhibits many discrete energy-loss peaks, which correspond to the quantization of electron energies. On the other hand, the AA-BLG spectra possess a unique and pronounced peak at low frequency. This peak represents the collective excitation of the entire low-frequency Landau states. The dependence of the energy-loss peaks on the momentum transfer and the magnetic field strength is presented. Accordingly, two kinds of plasmon modes produced by the layer stacking are clearly distinguished.

Abstract:
The electronic properties of hydrogenated graphenes are investigated with the first-principles calculations. Geometric structures, energy bands, charge distributions, and density of states (DOS) strongly depend on the different configurations and concentrations of hydrogen adatoms. Among three types of optimized periodical configurations, only in the zigzag systems the band gaps can be remarkably modulated by H-concentrations. There exist middle-gap semiconductors, narrow-gap semiconductors, and gapless systems. The band structures exhibit the rich features, including the destruction or recovery of the Dirac-cone structure, newly formed critical points, weakly dispersive bands, and (C,H)-related partially flat bands. The orbital-projected DOS are evidenced by the low-energy prominent peaks, delta-function-like peaks, discontinuous shoulders, and logarithmically divergent peaks. The DOS and spatial charge distributions clearly indicate that the critical bondings in C-C and C-H is responsible for the diversified properties.

Abstract:
Electronic properties of graphene oxides enriched by the strong chemical bondings are investigated using first-principle calculations. They are very sensitive to the changes in the number of graphene layer, stacking configuration, and distribution of oxygen. The feature-rich electronic structures exhibit the destruction or distortion of Dirac cone, opening of band gap, anisotropic energy dispersions, O- and (C,O)-dominated energy dispersions, and extra critical points. All the few-layer graphene oxides are semi-metals except for the semiconducting monolayer ones. For the former, the distorted Dirac-cone structures and the O-dominated energy bands near the Fermi level are revealed simultaneously. The orbital-projected density of states (DOS) have many special structures mainly coming from a composite energy band, the parabolic and partially flat ones. The DOS and spatial charge distributions clearly indicate the critical bondings in O-O, C-O and C-C bonds, being responsible for the diversified properties.

Abstract:
We use the tight-binding model and the random-phase approximation to investigate the intrinsic plasmon in silicene. At finite temperatures, an undamped plasmon is generated from the interplay between the intraband and the interband-gap transitions. The extent of the plasmon existence range in terms of momentum and temperature, which is dependent on the size of single-particle-excitation gap, is further tuned by applying a perpendicular electric field. The plasmon becomes damped in the interband-excitation region. A low damped zone is created by the field-induced spin split. The field-dependent plasmon spectrum shows a strong tunability in plasmon intensity and spectral bandwidth. This could make silicene a very suitable candidate for plasmonic applications.

Abstract:
A generalized tight-binding model, which is based on the subenvelope functions of the different sublattices, is developed to explore the novel magnetic quantization in monolayer gray tin. The effects due to the $sp^{3}$ bonding, the spin-orbital coupling, the magnetic field and the electric field are simultaneously taken into consideration. The unique magneto-electronic properties lie in two groups of low-lying Landau levels, with different orbital components, localization centers, state degeneracy, spin configurations, and magnetic- and electric-field dependences. The first and second groups mainly come from the $5p_{z}$ and ($5p_{x}$,$5p_{y}$) orbitals, respectively. Their Landau-level splittings are, respectively, induced by the electric field and spin-orbital interactions. The intragroup anti-crossings are only revealed in the former. The unique tinene Landau levels are absent in graphene, silicene and germanene.

Abstract:
Geometric and electronic properties of folded graphene nanoribbons (FGNRs) are investigated by first-principles calculations. These properties are mainly dominated by the competition or cooperation among stacking, curvature and edge effects. For the zigzag FGNRs, the more stable structures are revealed to be AB stackings, while for the armchair types, AA" stackings are more stable. The interlayer interactions and hybridization of four orbitals lead to smaller energy gaps, anti-crossing bands, and more band-edge states. Specifically, the broken mirror symmetry in the odd-AB stacked zigzag FGNRs is responsible for the spin-up and spin-down splitting subbands. All FGNRs are direct-gap semiconductors except that the edge-edge interactions cause the even-AA stacked zigzag FGNRs to exhibit a pair of metallic linear bands. The width-dependent energy gaps in the armchair FGNRs can be classified into six groups. Furthermore, there exist rich features in density of states, including the form, number, intensity and energy of the special structures.

Abstract:
A review work is done for electronic and optical properties of graphene nanoribbons in magnetic, electric, composite, and modulated fields. Effects due to the lateral confinement, curvature, stacking, non-uniform subsystems and hybrid structures are taken into account. The special electronic properties, induced by complex competitions between external fields and geometric structures, include many one-dimensional parabolic subbands, standing waves, peculiar edge-localized states, width- and field-dependent energy gaps, magnetic-quantized quasi-Landau levels, curvature-induced oscillating Landau subbands, crossings and anti-crossings of quasi-Landau levels, coexistence and combination of energy spectra in layered structures, and various peak structures in the density of states. There exist diverse absorption spectra and different selection rules, covering edge-dependent selection rules, magneto-optical selection rule, splitting of the Landau absorption peaks, intragroup and intergroup Landau transitions, as well as coexistence of monolayer-like and bilayer-like Landau absorption spectra. Detailed comparisons are made between the theoretical calculations and experimental measurements. The predicted results, the parabolic subbands, edge-localized states, gap opening and modulation, and spatial distribution of Landau subbands, have been verified by various experimental measurements.

Abstract:
The dispersion relation of the high energy optical \pi-plasmons of simple hexagonal intrinsic graphite was calculated within the self-consistent-field approximation. The plasmon frequency \omega_p is determined as functions of the transferred momentum $q_{\parallel}$ along the hexagonal plane in the Brillouin zone and its perpendicular component $q_z$. These plasmons are isotropic within the plane in the long wavelength limit. As the in-plane transferred momentum is increased, the plasmon frequency strongly depends on its magnitude and direction (\phi). With increasing angle, the dispersion relation within the hexagonal plane is gradually changed from quadratic to nearly linear form. There are many significant differences for the \pi-plasmon dispersion relations between 2D graphene and 3D AA-stacked graphite. They include $q_\parallel$- and \phi-dependence and \pi-plasmon bandwidth. This result reveals that interlayer interaction could enhance anisotropy of in-plane \pi-plasmons. For chosen $\textbf{q}_\parallel$, we also obtain the plasmon frequency as a function of $q_z$ and show that there is an upper bound on $q_z$ for plasmons to exist in graphite. Additionally, the group velocity for plasmon propagation along the perpendicular direction may be positive or negative depending on the choice of $\textbf{q}_\parallel$. Consequently, the forward and backward propagation of \pi-plasmons in AA-stacked graphite in which the energy flow is respectively parallel or antiparallel to the transferred momentum, can be realized. The backward flowing resonance is an intrinsic property of AA-stacked graphite, arising from the energy band structure and the interlayer coupling.

Abstract:
We derive the generalized magneto-absorption spectra for curved graphene nanorib- bons and carbon nanotubes by using the Peierls tight-binding model. The main spectral characteristics and the optical selection rules result from the cooperative or competitive relationships between the geometric structure and a magnetic ?eld. In curved ribbons, the dominant selection rule remains unchanged during the variation of the curvature. When the arc angle increases, the prominent peaks are split, with some even vanishing as the angle exceeds a critical value. In carbon nanotubes, the angular-momentum coupling induces extra selection rules, of which more are revealed due to the increase of either (both) of the factors: tube diameter and ?eld strength. Particularly once the two factors exceed certain critical values, the optical spectra could reflect the quasi-Landau-level structures. The identifying features of the spec- tra provide insight into optical excitations for curved systems with either open or closed boundary condition.

Abstract:
The magnetoelectronic properties of quasi-one-dimensional zigzag graphene nanoribbons are investigated by using the Peierls tight-binding model. Quasi-Landau levels (QLLs), dispersionless Landau subbands within a certain region of k-space, are resulted from the competition between magnetic and quantum confinement effects. In bilayer system, the interlayer interactions lead to two groups of QLLs, one occurring at the Fermi level and the other one occurring at higher energies. Transverse electric fields are able to distort energy spectrum, tilt two groups of QLLs and cause semiconductor-metal transition. From the perspective of wave functions, the distribution of electrons is explored, and the evolution of Landau states under the influence of electric fields is clearly discussed. More interestingly, the band mixing phenomena exhibited in the energy spectrum are related to the state mixing, which can be apparently seen in the wave functions. The density of states, which could be verified through surface inspections and optical experiments, such as scanning tunneling spectroscopy and absorption spectroscopy, is provided at last.