Modulation effects on Landau levels in a monolayer graphene

Magneto-optical properties of ABC-stacked trilayer graphene

The generalized tight-binding model is developed to investigate the magneto-optical absorption spectra of ABC-stacked trilayer graphene.

The selection rule of graphene in a composite magnetic field

The generalized tight-binding model with exact diagonalization method is developed to calculate the optical properties of monolayer graphene in the presence of composite magnetic fields. The ratio of the uniform magnetic field and the modulated one accounts for a strong influence on the structure, number, intensity and frequency of absorption peaks, and thus the extra selection rules that are subsequently induced can be explained. When the modulated field increases, each symmetric peak, under a uniform magnetic field, splits into a pair of asymmetric peaks with lower intensities. The threshold absorption frequency exhibits an obvious evolution in terms of a redshift. These absorption peaks obey the same selection rule that is followed by Landau level transitions. Moreover, at a sufficiently strong modulation strength, the extra peaks in the absorption spectrum might arise from different selection rules.

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.

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.

Thermodynamic properties of a weakly modulated graphene monolayer in a magnetic field

Theoretical investigation of thermodynamic properties of an electrically modulated graphene monolayer in the presence of a perpendicular magnetic field B is presented. This work is aimed at determining the modulation-induced effects on the thermodynamic properties of graphene. The results obtained are compared with those of conventional two-dimensional electron gas (2DEG) systems realized in semiconductor heterostructures. The one-dimensional periodic potential, due to electric modulation lifts the degeneracy of the Landau levels and converts them into bands whose width oscillates as a function of B. We find commensurability (Weiss) oscillations for small values of B and de Haas-van Alphen (dHvA)-type oscillations at larger values of B. We find that the modulation-induced effects on the thermodynamic properties are enhanced and less damped with temperature in graphene compared with conventional 2DEG systems. Furthermore, we have derived analytic asymptotic expressions which allow us to determine the critical temperature and critical magnetic field for the damping of magnetic oscillations in the thermodynamic quantities considered here.