ABSTRACT
A uniform perpendicular magnetic field plays a critical role on the essential physical properties. The magnetic quantization arising from B z Z ^ https://s3-euw1-ap-pe-df-pch-content-public-u.s3.eu-west-1.amazonaws.com/9780429277368/624878ab-52f4-47c3-a8bf-374018371aaa/content/unequ163-01.tif"/> belongs to a diverse but not monotonous phenomena [28-31,82,91,339,366-372]. This means that the Landau-level (LL) energy spectra greatly exhibit various B z -dependences and noncrossing/crossing/anticrossing behaviors during the variation of field strength [29,30,339], and the magnetowave functions apparently show regular or extremely irregular probability distribution with a specific zero-point number [30], the coexistent major and minor mode [82, 91], or the B z -dependent zero points [30], and the magneto-optical absorption spectra clearly present well-behaved and extra absorption selection rules [28, 31], the transport properties directly reveal the normal and unusual quantum Hall effects [366,368-372], and the magneto-Coulomb electron-electron (e-e) interactions obviously create rich and unique single-particle and collective excitations [32, 373-383]. The fundamental magnetoelectronic properties might be solved by the generalized model [28, 31] and the effective-mass model [12,318,327,369,384-386]. It should be noticed that the latter is very difficult to deal with the magnetically quantized states induced by the complex energy dispersions (e.g., the oscillatory, partially flat, and sombrero-shaped ones) [82, 339], the crossing/mixed energy bands [91], and the multipairs of valence and conduction bands near the Fermi level [82]. Unfortunately, most of the layered condensed-matter systems display such electronic structures. On the other hand, the former is successful in thoroughly exploring the diversified electronic, optical, transport, and Coulomb-excitation properties associated with the emergent 2D materials. For example, this model has conducted a full and systematic study on the few-layer graphene [28, 30, 31], silicene [29,387], germanene [29], phosphorene [29,388], and bismuthene [29,389]. Most important, the lattice symmetries, layer numbers, stacking configurations, planar/buckled structures, spin-orbital couplings, and single- and multior-bital hybridizations (hopping integrals) are taken into account simultaneously, being automatically consistent with the requirements of quantum statistics [29]. When the generalized tight-binding model is reformulated to link the linear static/dynamic Kubo formula, quantum transport behaviors/selection rules of absorption spectra could be obtained and analyzed. It is also combined with the modified random-phase approximation (RPA) to completely 164investigate novel magnetoelectronic excitations in layered graphene [23, 25]. Moreover, the concise physical pictures are proposed to comprehend the unusual essential properties.
