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.

This article reviews the rich magneto-electronic properties of multilayer graphene systems. Multilayer graphenes are built from graphene sheets attracting one another by van der Waals forces; the magneto-electronic properties are diversified by the number of layers and the stacking configurations. For an N-layer system, Landau levels are divided into N groups, with each identified by a dominant sublattice associated with the stacking configuration. We focus on the main characteristics of Landau levels, including the degeneracy, wave functions, quantum numbers, onset energies, field-dependent energy spectra, semiconductor-metal transitions, and crossing patterns, which are reflected in the magneto-optical spectroscopy, scanning tunneling spectroscopy, and quantum transport experiments. The Landau levels in AA-stacked graphene are responsible for multiple Dirac cones, while in AB-stacked graphene the Dirac properties depend on the number of graphene layers, and in ABC-stacked graphene the low-lying levels are related to surface states. The Landau-level mixing leads to anticrossings patterns in energy spectra, which are seen for intergroup Landau levels in AB-stacked graphene, while in particular, a formation of both intergroup and intragroup anticrossings is observed in ABC-stacked graphene. The aforementioned magneto-electronic properties lead to diverse optical spectra, plasma spectra, and transport properties when the stacking order and the number of layers are varied. The calculations are in agreement with optical and transport experiments, and novel features that have not yet been verified experimentally are presented.

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The feature-rich electronic excitations of monolayer germanene lie in the significant spin-orbit coupling and the buckled structure. The collective and single-particle excitations are diversified by the magnitude and direction of transferred momentum, the Fermi energy and the gate voltage. There are four kinds of plasmon modes, according to the unique frequency- and momentum-dependent phase diagrams. They behave as two-dimensional acoustic modes at long wavelength. However, for the larger momenta, they might change into another kind of undamped plasmons, become the seriously suppressed modes in the heavy intraband e–h excitations, keep the same undamped plasmons, or decline and then vanish in the strong interband e–h excitations. Germanene, silicene and graphene are quite different from one another in the main features of the diverse plasmon modes.

The low-lying Landau level (LL) properties of ABC-stacked trilayer graphene are investigated by the tight-binding (TB) model. The LL spectra exhibit an asymmetric structure around the Fermi level and three finely split LLs close to the Fermi level. The LL wave functions are described by six magnetic TB Bloch functions associated with six sublattices. These Bloch functions possess oscillation modes and localization features. An effective quantum number, which is used to define a LL, is defined by the oscillation mode of the Bloch function with the largest amplitude. The LL energies in the low-field and high-field regions exhibit different features since the trigonal warping effect strongly dominates the LL properties in the low-field region. Furthermore, the LLs do not present a simple relation between the magnetic field strength (effective quantum number) and the LL energy. A detailed comparison of the calculation with all atomic interactions taken into account and that ignoring some interlayer interactions is offered. The dissimilarities between these two calculations demonstrate that interlayer interactions strongly affect the main features of LLs and should not be ignored. The dissimilarities could be further examined by experimental measurements.

The feature-rich electronic and magnetic properties of fluorine-doped graphene nanoribbons are investigated by the first-principles calculations. They arise from the cooperative or competitive relations among the significant chemical bonds, finite-size quantum confinement and edge structure. There exist C-C, C-F, and F-F bonds with multi-orbital hybridizations. Fluorine adatoms can create p-type metals or concentration- and distribution-dependent semiconductors, depending on whether the π bonding is seriously suppressed by the top-site chemical bonding. Furthermore, five kinds of spin-dependent electronic and magnetic properties cover the non-magnetic and ferromagnetic metals, non-magnetic semiconductors, and anti-ferromagnetic semiconductors with/without spin splitting. The diverse essential properties are clearly revealed in the spatial charge distribution, spin density, and orbital-projected density of states.

Diverse magnetic and electronic properties of halogen-adsorbed silicene are investigated by the first-principle theoretical framework, including the adatom-diversified geometric structures, atom-dominated energy bands, spatial spin density distributions, spatial charge density distributions and its variations, and orbital-projected density of states. Also, such physical quantities are sufficient to identify similar and different features in the double-side and single-side adsorptions. The former belongs to the concentration-depended finite gap semiconductors or p-type metals, while the latter display the valence energy bands with/without spin-splitting intersecting with the Fermi level. Both adsorption types show the halogen-related weakly dispersed bands at deep energies, the adatom-modified middle-energy σ bands, and the recovery of low-energy π bands during the decrease of the halogen concentrations. Such feature-rich band structures can be verified by the angle-resolved photoemission spectroscopy experiment.