The effect of perpendicular electric field $\left(\mathbf{F}\right)$ on optical properties of the AB-stacked few-layer graphene, made up of two, three, or four graphite sheets, is explored through the gradient approximation. In contrast to the featureless optical spectra of graphene, the low-energy absorption spectra of few-layer graphene with AB stacking exhibit many jumping structures, which result from the band-edge states caused by the stacking effect, in the absence of an electric field. Remarkably, $\mathbf{F}$ causes the subband (anti)crossing, changes the subband spacing, produces the oscillating bands, and increases the band-edge states. It, therefore, follows that the field-modulating spectra with sharp peaks are generated. Moreover, the frequency of peak, which is strongly dependent on the layer number and the field strength, is predicted. Above all, the predicted absorption spectra and the associated electronic properties could be verified by the optical measurements.

A review work is done for the electronic and optical properties of graphene nanoribbons in magnetic, electric, composite, and modulated fields.

The Peierls Hamiltonian band matrix is developed to investigate magnetoelectronic properties of bilayer Bernal graphene. A uniform perpendicular magnetic field creates many dispersionless Landau levels (LLs) at low and high energies and some oscillatory LLs at moderate energy. State degeneracy of the low LLs is two times as much as that of the high LLs. Wave functions and state energies are dominated by the interlayer atomic interactions and field strength $\left(B_0\right)$. The former induce two groups of LLs, more low LLs, the asymmetric energy spectrum about the Fermi level, and the change of level spacing. Two sets of effective quantum numbers, $n_1^{\mathit{eff}}$’s and $n_2^{\mathit{eff}}$’s, are required to characterize all the wave functions. They are determined by the strongest oscillation modes of the dominant carrier densities; furthermore, they rely on the specific interlayer atomic hoppings. The dependence of the quite low Landau-level energies on $B_0$ and $n_1^{\mathit{eff}}$ is approximately linear. An energy gap is produced by the magnetic field and interlayer atomic hoppings. $E_g$ grows with increasing field strength, while it is reduced by the Zeeman effect. The main features of magnetoelectronic structures are directly reflected in the density of states. The predicted electronic properties could be verified by the experimental measurements on absorption spectra and transport properties.

We used first-principles calculations to investigate the electrical and optical properties of CsGeX₃ (X = Cl, Br, and I) compounds. These materials present rich and unique physical and chemical phenomena, such as the optimal geometric structure, the electronic band structure, the charge density distribution, and the special van Hove singularities in the electronic density of states. The optical properties cover a slight red shift of the optical gap, corresponding to weak electron-hole interactions, strong absorption coefficients, and weak reflectance spectra. The presented theoretical framework will provide a full understanding of the various phenomena and promising applications for solar cells and other electro-optic materials.

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 = J^c – J^v = 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.

The magneto-optical absorption spectra of AA-stacked bilayer graphene (AABG) exhibit two kinds of absorption peaks resulting from two groups of Landau levels (LLs). Only intragroup excitations that follow a single selection rule take place. The excitation channels are altered as the field strength approaches a critical strength. These optical properties can be comprehended by the characteristics of the LL wave functions. A comparison of AABG and AB-stacked bilayer graphene (BBG) demonstrates that the optical properties are dominated by the stacking symmetry. The presented results could offer a way to distinguish AABG from BBG and monolayer graphene.