Yen-Hung Ho

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 properties of deformed few-layer graphenes with AB stacking

Optical excitations of deformed AB-stacked graphenes are studied through the gradient approximation. The interlayer atomic interactions induce prominent peaks, shoulder structures, and transition gaps in the low-energy absorption spectra. The uniaxial stress changes the energy spacing at the band-edge states and the Fermi momenta, which reflects on the spectrum peak frequencies and the transition gaps, respectively. These optical characteristics are also influenced by the layer number. Besides, deformation shows some similar and different effects in comparison with electric and magnetic fields. These predicted optical properties can be verified by optical measurements.

Optical properties of BC3 nanotubes

Optical absorption spectra of BC3 nanotubes are studied within the gradient approximation. BC3 nanotubes exhibit rich absorption peaks in the overall frequency because of a lot of one-dimensional energy bands. The threshold absorption frequency is ∼0.15γ0 for all BC3 nanotubes. Absorption peaks are mainly determined by the chirality, radius, and magnetic flux. BC3 nanotubes quite differ from carbon nanotubes in the low- and high-frequency absorption spectra. The calculated results are roughly consistent with the optical measurements, such as the threshold absorption frequency and the existence of the low-frequency absorption peaks.

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.

Haldane model under nonuniform strain

We study the Haldane model under strain using a tight-binding approach, and compare the obtained results with the continuum-limit approximation. As in graphene, nonuniform strain leads to a time-reversal preserving pseudo-magnetic field that induces (pseudo) Landau levels. Unlike a real magnetic field, strain lifts the degeneracy of the zeroth pseudo Landau levels at different valleys. Moreover, for the zigzag edge under uniaxial strain, strain removes the degeneracy within the pseudo-Landau levels by inducing a tilt in their energy dispersion. The latter arises from next-to-leading order corrections to the continuum-limit Hamiltonian, which are absent for a real magnetic field. We show that, for the lowest pseudo-Landau levels in the Haldane model, the dominant contribution to the tilt is different from graphene. In addition, although strain does not strongly modify the dispersion of the edge states, their interplay with the pseudo-Landau levels is different for the armchair and zigzag ribbons. Finally, we study the effect of strain in the band structure of the Haldane model at the critical point of the topological transition, thus shedding light on the interplay between non-trivial topology and strain in quantum anomalous Hall systems.