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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.

A review work is done for the electronic and optical properties of graphene nanoribbons in magnetic, electric, composite, and modulated fields. Effects due to the lateral confinement, curvature, stacking, non-uniform subsystems and hybrid structures are taken into account. The special electronic properties, induced by complex competitions between external fields and geometric structures, include many one-dimensional parabolic subbands, standing waves, peculiar edge-localized states, width- and field-dependent energy gaps, magnetic-quantized quasi-Landau levels, curvature-induced oscillating Landau subbands, crossings and anti-crossings of quasi-Landau levels, coexistence and combination of energy spectra in layered structures, and various peak structures in the density of states. There exist diverse absorption spectra and different selection rules, covering edge-dependent selection rules, magneto-optical selection rule, splitting of the Landau absorption peaks, intragroup and intergroup Landau transitions, as well as coexistence of monolayer-like and bilayer-like Landau absorption spectra. Detailed comparisons are made between the theoretical calculations and experimental measurements. The predicted results, the parabolic subbands, edge-localized states, gap opening and modulation, and spatial distribution of Landau subbands, have been identified by various experimental measurements.

A detailed study of the elementary excitations of an electron gas confined to a tubule system is presented. The system could consist either of a single cylindrical tubule or of several tubules sharing a 0 common axis. Graphene tubules with a radius as small as 11 A have been recently realized. Essential features revealed from this study are expected to be common to the graphene tubules. The dielectric function of the quasi-one-dimensional (1D) tubular system has been evaluated exactly within the random-phase approximation, where both the intrasubband and the intersubband excitations are included. The angular momentum (L) is conserved in the tubule system. The excitations, e.g. , plasmons, of different L's are thus mutually decoupled. At any given L, only a small number of plasmon branches exist, every one of which can be studied systematically. Intertubule interaction for coaxial tubules has been included. The coupling among coaxial tubules adds unique features that distinguish the tubules from other quasi-1D systems.