C. P. Chang

Magnetic and quantum confinement effects on electronic and optical properties of graphene ribbons.

Through the tight-binding calculation, we demonstrate that magnetic and quantum confinements have a great influence on the low-energy band structures of one-dimensional (1D) armchair graphene ribbons. The magnetic field first changes 1D parabolic bands into the Hall-edge states which originate in the Landau wavefunctions deformed by one or two ribbon edges. The quantum confinement dominates the characteristics of the Hall-edge states only when the Landau wavefunctions touch two ribbon edges. Then, some of the Hall-edge states evolve as the Landau states when the field strength grows. The partial flat bands (Landau levels), related to the Landau states, appear. The magnetic field dramatically modifies the energy dispersions and it changes the size of the bandgap, shifts the band-edge states, destroys the degeneracy of the energy bands, induces the semiconductor-metal transition and generates the partial flat bands. The above-mentioned magneto-electronic properties are completely reflected in the low-frequency absorption spectra--the shift of peak position, the change of peak symmetry, the alteration of peak height, the generation of new peaks and the change of absorption edges. As a result, there are magnetic-field-dependent absorption frequencies. The findings show that the magnetic field could be used to modulate the electronic properties and the absorption spectra.

Low-energy electronic properties of the AB-stacked few-layer graphites

In the presence of a perpendicular electric field, the low-energy electronic properties of the AB-stacked N-layer graphites with layer number N = 2, 3, and 4, respectively, are examined through the tight-binding model. The interlayer interactions, the number of layers, and the field strength are closely related to them. The interlayer interactions can significantly change the energy dispersions and produce new band-edge states. Bi-layer and four-layer graphites are two-dimensional semimetals due to a tiny overlap between the valence and conduction bands, while tri-layer graphite is a narrow-gap semiconductor. The electric field affects the low-energy electronic properties: the production of oscillating bands, the cause of subband (anti)crossing, the change in subband spacing, and the increase in band-edge states. Most importantly, the aforementioned effects are revealed completely in the density of states, e.g. the generation of special structures, the shift in peak position, the change in peak height, and the alteration of the band gap.

Electronic properties of AA- and ABC-stacked few-layer graphites

The low-energy electronic properties of a few graphite layers with AA and ABC stacking under application of the electric field (F), perpendicular to the layers, are explored through the tight-binding model. They strongly depend on the interlayer interactions, the stacking sequences, the layer numbers, and the field strength. In the absence or presence of F, the AA-stacked N-layer graphites (N ¼ 3 and 4) exhibit the linear bands near the Fermi energy. The interlayer interactions and electric field chiefly shift the Fermi momenta and the state energies. The ABC-stacked N-layer graphites are characterized by the complicated low-energy bands due to the stacking effect, on which F has a great influence—the change of the state energies and the subband spacing, the opening of a band gap, the production of the oscillating bands, and the increase of the band-edge states. As a result, the two kinds of special structure, whose positions and heights are modulated by F, are found in the density of states (DOS) in contrast to the featureless DOS of the AA systems. The comparison with the AB-stacked few-layer graphites is also made.

Deformation effect on electronic and optical properties of nanographite ribbons

The electronic structures of deformed nanographite ribbons are calculated from the Huckel tight-binding model. They strongly depend on the uniaxial strain and the ribbon geometry (edge structure and width). The uniaxial strain significantly affects the subband spacings and the energy dispersions. A monotonous relation between the uniaxial strain and the state energies is absent. For armchair ribbons, the uniaxial strain drastically changes the energy gap and thus leads to the semiconductor-metal transition. The dependence of energy gap on strain is determined by the ribbon width. The large strain could also induce the subband crossing. On the other hand, zigzag ribbons remain metallic during the variation of the strain. Armchair and zigzag ribbons, respectively, behave as zigzag and armchair nanotubes. The calculated absorption spectrum exhibits rich peak structures, mainly owing to the divergent density of states of the one-dimensional subbands. The uniaxial-strain effects on optical excitations are stro...

Landau levels and magneto-optical properties of graphene ribbons

On the basis of Peierl coupling tight-binding model, we study the low energy magnetoelectronic properties of zigzag graphene ribbons by changing the ribbon width from the nanometer to the mesoscopic scale. The evolution of the Landau levels with the ribbon width shows that the number and the range of Landau levels are chiefly dominated by the ribbon width and the magnetic field (B). The Landau-level energies abide by the simple relation ∣E∣∝∣n∣B at low energy, not at the high energy (n subband index). However, a scaling law between the number of Landau levels and the ribbon width cannot be figured out. The Landau states occur only when the ribbon width is close to or greater than the distribution width of the Landau wave function and more Landau levels are generated with the increase in width. The low-frequency magnetoabsorption spectra reveal electronic properties and, thus, exhibit distinguishable delta-function-like peaks (Landau peaks). The peak height runs higher when the width increases, for more La...

Optical spectra of AB- and AA-stacked nanographite ribbons

The absorption spectra of the AB- and AA-stacked nanographite ribbons have several prominent peaks. They strongly depend on the edge structure, the ribbon width, the stacking sequence, and the polarization direction. The armchair ribbons quite differ from the zigzag ribbons. The frequency and the number of the absorption peaks are affected by the ribbon width. The AB-stacked systems have lower threshold absorption frequency, more absorption peaks, and weaker spectral intensity, as compared with the AA-stacked systems. The absorption spectra are highly anisotropic. The optical excitations of the parallel polarization (E∥ ∥ z) are absent in the AA-stacked systems. Comparison with graphite is discussed.

Optical excitations of boron nitride ribbons and nanotubes

Abstract The π-electronic structures of boron nitride ribbons and nanotubes are obtained from the tight-binding model. The absorption spectra are studied within the gradient approximation. They exhibit the prominent absorption peaks, mainly owing to the divergent density of states. The spectral intensity, the number of absorption peaks, and the excitation energies strongly depend on the geometry structures (ribbons or nanotubes, and zigzag structures or armchair structures). The characteristics of absorption spectra are associated with the selection rule and the state degeneracy. The 1D boron nitride systems, the zigzag ribbons excepted, have the same selection rule.

Exploration of edge-dependent optical selection rules for graphene nanoribbons

Optical selection rules for one-dimensional graphene nanoribbons are explored based on the tight-binding model. A theoretical explanation, through analyzing the velocity matrix elements and the features of the wavefunctions, can account for the selection rules, which depend on the edge structure of the nanoribbon, i.e., armchair or zigzag edges. The selection rule of armchair nanoribbons is ΔJ = Jc - Jv = 0, and the optical transitions occur from the conduction to the valence subbands of the same index. Such a selection rule originates in the relationships between two sublattices and between the conduction and valence subbands. On the other hand, zigzag nanoribbons exhibit the selection rule |ΔJ| = odd, which results from the alternatively changing symmetry property as the subband index increases. Furthermore, an efficient theoretical prediction on transition energies is obtained by the application of selection rules, and the energies of the band-edge states become experimentally attainable via optical measurements.Optical selection rules for one-dimensional graphene nanoribbons are analytically studied and clarified based on the tight-binding model. A theoretical explanation, through analyzing the velocity matrix elements and the features of wavefunctions, can account for the selection rules, which depend on the edge structure of nanoribbon, namely armchair or zigzag edges. The selection rule of armchair nanoribbons is ∆J = J − J = 0, and the optical transitions occur from the conduction to valence subbands of the same index. Such a selection rule originates in the relationships between two sublattices and between conduction and valence subbands. On the other hand, zigzag nanoribbons exhibit the selection rule |∆J | = odd, which results from the alternatively changing symmetry property as the subband index increases. An efficiently theoretical prediction on transition energies is obtained with the application of selection rules. Furthermore, the energies of band edge states become experimentally attainable via optical measurements.

Magnetoconductance of graphene nanoribbons

The electronic and transport properties of monolayer and AB-stacked bilayer zigzag graphene nanoribbons subject to the influences of a magnetic field are investigated theoretically. We demonstrate that the magnetic confinement and the size effect affect the electronic properties competitively. In the limit of a strong magnetic field, the magnetic length is much smaller than the ribbon width, and the bulk electrons are confined solely by the magnetic potential. Their properties are independent of the width, and the Landau levels appear. On the other hand, the size effect dominates in the case of narrow ribbons. In addition, the dispersion relations rely sensitively on the interlayer interactions. Such interactions will modify the subband curvature, create additional band-edge states, change the subband spacing or the energy gap, and separate the partial flat bands. The band structures are symmetric or asymmetric about the Fermi energy for monolayer or bilayer nanoribbons, respectively. The chemical-potential-dependent electrical and thermal conductance exhibits a stepwise increase behaviour. The competition between the magnetic confinement and the size effect will also be reflected in the transport properties. The features of the conductance are found to be strongly dependent on the field strength, number of layers, interlayer interactions, and temperature.

Optical Properties of Boron Nitride Nanotubes

Optical properties of single-walled boron nitride nanotubes have been studied theoretically. The dielectric functions calculated from the gradient approximation and the random-phase approximation are consistent with each other. The imaginary and the real parts of the dielectric function, respectively, exihibit the special peaks and dips. The strong e-h absorption peaks at ω < 4 γ 0 comes from the π band and the others from the π + a bands (γ 0 is the nearest-neighbor interaction of 2p z orbitals). Such single-particle excitations also induce the peak structures in the reflectance spectrum. On the other hand, the loss function shows the prominent π- and π + σ-plasmon peaks. The π and π + a plasmons (collective excitations) reveal themselves in the reflectance spectrum as strong and abrupt edges. The optical properties are affected by the polarization direction and the nanotube radius, but not the chiral angle. The calculated results could be experimentally checked with optical spectroscopies or EELS.