Yu-Huang Chiu

Magneto-optical selection rules in bilayer Bernal graphene

The low-frequency magneto-optical properties of bilayer Bernal graphene are studied by the tight-binding model with the four most important interlayer interactions taken into account. Since the main features of the wave functions are well-depicted, the Landau levels can be divided into two groups based on the characteristics of the wave functions. These Landau levels lead to four categories of absorption peaks in the optical absorption spectra. Such absorption peaks own complex optical selection rules, and these rules can be reasonably explained by the characteristics of the wave functions. In addition, twin-peak structures, regular frequency-dependent absorption rates, and complex field-dependent frequencies are also obtained in this work. The main features of the absorption peaks are very different from those in monolayer graphene and have their origin in the interlayer interactions.

Optical transitions between Landau levels: AA-stacked bilayer graphene

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.

Electronic and optical properties of monolayer and bilayer graphene

The electronic and optical properties of monolayer and bilayer graphene are investigated to verify the effects of interlayer interactions and external magnetic field. Monolayer graphene exhibits linear bands in the low-energy region. Then the interlayer interactions in bilayers change these bands into two pairs of parabolic bands, where the lower pair is slightly overlapped and the occupied states are asymmetric with respect to the unoccupied ones. The characteristics of zero-field electronic structures are directly reflected in the Landau levels. In monolayer and bilayer graphene, these levels can be classified into one and two groups, respectively. With respect to the optical transitions between the Landau levels, bilayer graphene possesses much richer spectral features in comparison with monolayers, such as four kinds of absorption channels and double-peaked absorption lines. The explicit wave functions can further elucidate the frequency-dependent absorption rates and the complex optical selection rules. These numerical calculations would be useful in identifying the optical measurements on graphene layers.

Diagonalization of Landau Level Spectra in Rhombohedral Graphite

The Landau level (LL) spectra in rhombohedral graphite are calculated within the tight-binding model without any perturbation expansion. All significant interlayer atomic interactions are included, up to next-nearest-neighbor graphene layers. The magnetic Hamiltonian matrix is derived and manipulated in a band-like form for numerical efficiency. The results of this diagonalization scheme manifest the effects of lattice symmetry and interlayer interaction in the specific stacking configuration. Three-dimensional character associated with the mirror symmetry of the ABC-stacking configuration is exhibited in the LL spectra.

Magneto-absorption spectra of Bernal graphite

With the availability of Landau wave functions in real space, we investigate the magneto-optical spectra of ordinary bulk graphite within a tight-binding model. The interlayer interactions significantly affect the structure, frequency and intensity of absorption peaks, as well as their field evolution and the double-peak absorptions. Those unique features of the absorption constitute important characterization of graphite and serve to differentiate the bulk spectra from those of true monolayer and bilayer graphenes.

Optical-absorption spectra of single-layer graphene in a periodic magnetic field

The low-frequency magnetoelectronic properties of single-layer graphene in a periodic magnetic field are studied by the gradient approximation within the Peierls tight-binding model. A modulated magnetic field along the zigzag direction is chosen for a detailed investigation of optical absorption spectra. The electric polarization is taken to be perpendicular to the modulated direction. The absorption spectra exhibit many prominent and inconspicuous asymmetric peaks. They result from the transitions of the original and extra band-edge states, respectively. The prominent peaks are discussed in detail and they obey a simple optical selection rule, Δn=|nv−nc|=1, similar to that in a uniform magnetic field. Such a rule can be ascribed to certain characteristics of the wave functions. The energy of the prominent peaks strongly depends on the strength, while it exhibits little dependence on the period. The abovementioned results can be verified by optical measurements.

Electric modulation effect on magneto-optical spectrum of monolayer graphene

Abstract The generalized tight-binding model is developed to largely reduce the numerical computation time in calculating optical properties. Modulated electric potentials can control the low-frequency magneto-optical absorption spectra of monolayer graphene. They induce the oscillatory energy dispersions of Landau subbands and the spatial symmetry breaking of the wave function; therefore, the original peaks and extra peaks of different selection rules come into existence simultaneously. Such peaks mainly arise from the band-edge states and/or the middle states. Their number, intensities, frequencies and structures are dominated by the modulation strength and period. More absorption peaks appear with an increase in potential. The extra peaks can relatively easily be observed for higher frequencies and stronger potentials. However, the absorption spectra remain unchanged for a fixed ratio of strength over period.

Modulation Effects of Periodic Potentials on the Electronic Properties of Bilayer Bernal Graphene: Tight-Binding Model

Electronic properties of bilayer Bernal graphene under modulated electric fields are calculated by the tight-binding model with an exact diagonalization method. This approach efficiently calculates the energy bands, wave functions and densities of states (DOS). Such electronic properties are highly correlated to the strength, period and direction of the electric field. The interlayer atomic interactions result in two groups of subbands, and these subbands are significantly influenced by the electric fields, such as altered energy dispersions, strengthened overlapping, broken degeneracy, and a great amount of induced band-edge states. The electric fields also change main features of the wave functions, including the number of zero points, distribution symmetry, and standing-wave-like feature. The DOS at the Fermi energy rises with the growing field strength, but is not susceptible to the field period. Furthermore, the electric fields reveal different impacts on the two groups of subbands.

Magnetoelectronic and Optical Properties of Monolayer and AB-Stacked Bilayer Graphenes

The low-frequency magneto-absorption spectra of monolayer and bilayer graphene are evaluated within the gradient approximation. On the basis of Peierls tight-binding model, we can draw the wave function distribution over its sublattices and bring them into the calculation of optical spectra. The optical selection rules and the absorption rate can be accurately determined. The interlayer interactions in bilayers effectively alter the Landau level structures and thus the absorption spectra, such as the field dependence of absorption lines and the appearance of double-peaked absorptions.