We developed the generalized tight-binding model to study the magneto-electronic properties of AAB-stacked trilayer graphene. Three groups of Landau levels (LLs) are characterized by the dominating subenvelope function on distinct sublattices. Each LL group could be further divided into two sub-groups in which the wavefunctions are, respectively, localized at 2/6 (5/6) and 4/6 (1/6) of the total length of the enlarged unit cell. The unoccupied conduction and the occupied valence LLs in each subgroup behave similarly. For the first group, there exist certain important differences between the two sub-groups, including the LL energy spacings, quantum numbers, spatial distributions of the LL wavefunctions, and the field-dependent energy spectra.The LL crossings and anticrossings occur frequently in each sub-group during the variation of field strengths, which thus leads to the very complex energy spectra and the seriously distorted wavefunctions. Also, the density of states (DOS) exhibits rich symmetric peak structures. The predicted results could be directly examined by experimental measurements. The magnetic quantization is quite different among the AAB-, AAA-, ABA-, and ABC-stacked configurations.

The generalized tight-binding model is developed to investigate the rich and unique electronic properties of AB-bt (bottom-top) bilayer silicene under uniform perpendicular electric and magnetic fields. The first pair of conduction and valence bands, with an observable energy gap, displays unusual energy dispersions. Each group of conduction/valence Landau levels (LLs) is further classified into four subgroups, that is, there exist the sublattice-and spin-dominated LL subgroups. The magnetic-field-dependent LL energy spectra exhibit irregular behavior corresponding to the critical points of the band structure. Moreover, the electric field can induce many LL anti-crossings. The main features of the LLs are uncovered with many van Hove singularities in the density-of-states and non-uniform delta-function-like peaks in the magneto-absorption spectra. The feature-rich magnetic quantization directly reflects the geometric symmetries, intra-layer and inter-layer atomic interactions, spin-orbital couplings, and the field effects. The results of this work can be applied to novel designs of Si-based nano-electronics and nano-devices with enhanced mobilities.

A generalized tight-binding model is developed to investigate the feature-rich magneto-optical properties of AAB-stacked trilayer graphene. Three intragroup and six intergroup inter-Landau-level (inter-LL) optical excitations largely enrich magneto-absorption peaks. In general, the former are much higher than the latter, depending on the phases and amplitudes of LL wavefunctions. The absorption spectra exhibit single- or twin-peak structures which are determined by quantum modes, LL energy spectra and Fermion distribution. The splitting LLs, with different localization centers (2/6 and 4/6 positions in a unit cell), can generate very distinct absorption spectra. There exist extra single peaks because of LL anti-crossings. AAB, AAA, ABA, and ABC stackings considerably differ from one another in terms of the inter-LL category, frequency, intensity, and structure of absorption peaks. The main characteristics of LL wavefunctions and energy spectra and the Fermi-Dirac function are responsible for the configuration-enriched magneto-optical spectra.

The generalized tight-binding model is developed to investigate the magneto-optical absorption spectra of ABC-stacked trilayer graphene. The absorption peaks can be classified into nine categories of inter-Landau-level optical excitations, including three intra-group and six inter-group ones. Most of them belong to the twin-peak structures because of the asymmetric Landau level spectrum. The threshold absorption peak alone comes from a certain excitation channel, and its frequency is associated with a specific interlayer atomic interaction. The Landau-level anticrossings cause extra absorption peaks. Moreover, a simple relationship between the absorption frequency and the field strength is absent. The magneto-optical properties of ABC-stacked trilayer graphene are totally different from those of AAA- and ABA-stacked ones, such as the number, intensity and frequency of absorption peaks.

Optical properties of graphene are explored by using the generalized tight-binding model. The main features of spectral structures, the form, frequency, number and intensity, are greatly enriched by the complex relationship among the interlayer atomic interactions, the magnetic quantization and the Coulomb potential energy. Absorption spectra have shoulders, asymmetric peaks and logarithmic peaks, coming from the band-edge states of parabolic dispersions, the constant-energy loops and the saddle points, respectively. The initial forbidden excitation region is only revealed in even-layer AA stacking systems. Optical gaps and special structures can be generated by an electric field. The delta-function-like structures in magneto-optical spectra, which present the single, twin and double peaks, are associated with the symmetric, asymmetric and splitting Landau-level energy spectra, respectively. The single peaks due to the non-tilted Dirac cones exhibit the nearly uniform intensity. The AAB stacking possesses more absorption structures, compared to the other stackings. The diverse magneto-optical selection rules are mainly determined by the well-behaved, perturbed and undefined Landau modes. The frequent anti-crossings in the magneticand electric-field-dependent energy spectra lead to the increase of absorption peaks and the reduced intensities. Part of theoretical calculations are consistent with the 1 arXiv:1603.02797v2 [physics.comp-ph] 19 Jul 2016 experimental measurements, and the others need further detailed examinations.Graphene is a 2D material made up of hexagonal carbon lattices [1,2]. Since mono-and few-layer graphene sheets were first fabricated in 2004 [1,2], low-dimensional graphenerelated systems have been a great interest to experimental and theoretical studies. The stacking orders of graphene sheets include the essential sequences of AA [3,4], AB [5-9], ABC [5,[8][9][10][11] stackings. While the AA stacking configuration has only been artificially made from intercalated graphite compounds, the AB and ABC configurations are the common orders in natural graphite, respectively, with their estimated volume fractions: 80 % and 14 % [15,16]. The rest parts ∼ 6% consist of haphazardly stacked graphene sheets, called turbostratic configuration [17][18][19]. Few-layer graphene desired with a specific stacking configuration can be exfoliated from highly orientated pyrolytic graphite [1,2], and chemically and electrochemically reduced from graphene oxide [20][21][22][23][24][25][26][27]. Nevertheless, chemical vapor deposition method has the advantage of producing large-scale size of highquality graphene sheets. Recently, large area of graphene with high mobility and highly symmetric configurations, e.g., AA, AB and ABC, have been found in CVD-grown samples [28][29][30][31][32][33][34][35][36][37][38][39][40]. The improved quality is adequate for research experiments and industry applications [41][42][43][44][45][46][47][48][49][50]. In addition, the AAB stacking and intermediate bilayer configurations, with r...

The excited conduction electrons, conduction holes and valence holes in monolayer germanene exhibit the feature-rich Coulomb decay rates. The dexcitation processes are studied using the Matsubara's screened exchange energy. They might utilize the intraband single-particle excitations (SPEs), the interband SPEs, and three kinds of plasmon modes, depending on the quasiparticle states and the Fermi energies. The low-lying valence holes can decay by the undamped acoustic plasmon, so that they present very fast Coulomb deexcitations, the non-monotonous energy dependence and the anisotropic behavior. However, the low-energy conduction holes and electrons behave as 2D electron gas. The high-energy conduction states and the deep-energy valence ones are similar in the available deexcitation channels and the dependence of decay rate on wave vector k.A lot of two-dimensional (2D) materials have been successfully synthesized since the first discovery of graphene in 2004 using the mechanical exfoliation of Bernal graphite [1]. They are very suitable for exploring the diverse physical, chemical, and material properties. Specifically, the 2D IV-group systems possess the high-symmetry honeycomb lattice and the nano-scaled thickness, in which few-layer graphenes have been verified to exhibit the rich and unique properties, such as the massless/massive fermions [2-5], the quantized Landau levels [6-9], the magneto-optical selection rules [10-13], and the quantum Hall effects [14-17]. Recently, few-layer germanene, silicene and tinene are, respectively, grown on [Pt(111), Au(111) & Al(111)] surfaces [18-21], [Ag(111), Ir(111) & ZrBi 2 ] surfaces [22-24], and Bi 2 Te 3 (111) surface [25]. Such systems possess the buckled structures and the significant spin-orbital couplings (SOCs), leading to the dramatic changes in the essential properties. They are expected to present the unusual Coulomb excitations/deexcitations arising from many-particle electron-electron interactions. The Coulomb scattering rates of the excited states in monolayer germanene is chosen for a model study in this work, especially for their relations with the single-particle and collective electronic excitations. For germanene, silicene and graphene, the low-lying electronic structures mainly arise from the outmost p z orbitals [4, 26]. The Dirac-cone structures, being created by the hexagonal symmetry, might be separated or gapless as a result of the significant/negligible SOCs. The former two are predicted to be narrow-gap semiconductors (E g ∼ 93 meV for Ge & ∼7.9 meV for Si), reflecting the strength of SOC [26]. However, graphene has linear valence and conduction bands intersecting at the Dirac point in the absence of SOC.The predicted band structures could be verified from the angle-resolved photoemission spectroscopy (ARPES) measurements, as done for few-layer germanene grown on Au (111) surface [20]. The experimental observations show that the multiple Dirac-like energy dispersions might be caused by the folding of germanene's Dirac cones. The high-resolution...

We conduct a comprehensive investigation of the effect of an applied electric field on the optical and magneto-optical absorption spectra for AB-bt (bottom-top) bilayer silicene. The generalized tight-binding model in conjunction with the Kubo formula is efficiently employed in the numerical calculations. The electronic and optical properties are greatly diversified by the buckled lattice structure, stacking configuration, intralayer and interlayer hopping interactions, spin-orbital couplings, as well as the electric and magnetic fields ( ). An electric field induces spin-split electronic states, a semiconductor-metal phase transitions and the Dirac cone formations in different valleys, leading to the special absorption features. The Ez-dependent low-lying Landau levels possess lower degeneracy, valley-created localization centers, peculiar distributions of quantum numbers, well-behaved and abnormal energy spectra in Bz-dependencies, and the absence of anti-crossing behavior. Consequently, the specific magneto-optical selection rules exist for diverse excitation categories under certain critical electric fields. The optical gaps are reduced as Ez is increased, but enhanced by Bz, in which the threshold channel might dramatically change in the former case. These characteristics are in sharp contrast with those for layered graphene.

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