Feature-Rich Magnetic Quantization in Sliding Bilayer Graphenes

Abstract

The generalized tight-binding model, based on the subenvelope functions of distinct sublattices, is developed to investigate the magnetic quantization in sliding bilayer graphenes. The relative shift of two graphene layers induces a dramatic transformation between the Dirac-cone structure and the parabolic band structure, and thus leads to drastic changes of Landau levels (LLs) in the spatial symmetry, initial formation energy, intergroup anti-crossing, state degeneracy and semiconductor-metal transition. There exist three kinds of LLs, i.e., well-behaved, perturbed and undefined LLs, which are characterized by a specific mode, a main mode plus side modes, and a disordered mode, respectively. Such LLs are clearly revealed in diverse magneto-optical selection rules. Specially, the undefined LLs frequently exhibit intergroup anti-crossings in the field-dependent energy spectra, and show a large number of absorption peaks without optical selection rules.

Introduction

“…The former two show multiple Dirac cone dispersions and the superposition of monolayer-like and bilayer-like dispersions respectively [8], while the latter is not analogous to the AA and AB configurations [68,70]. On the other hand, the deformation of Dirac cones for the AAB-and sliding bilayer configurations [64,66,148] can be verified by using ARPES. The aforementioned electronic characteristics have also been confirmed in absorption [164, 166-168, 173, 174, 177], transmission [180,181], refection [136], Raman scattering and Rayleigh scattering spectroscopy [75,76,138,139,171,172,[236][237][238][239][240][241][242][243].…”

“…An intermediate bilayer configuration is formed from AA to AB, and then to AA′, as the two graphene sheets shift relative to each other in the armchair direction [66,148]. The two Dirac cones transform into parabolic bands from AA to AB configurations, and for a further layer-layer shift, they tilt towards each other at a small angle, restoring the AA′ configuration.…”

“…Regarding the latter, one can use optical spectroscopy to identify the non-monotonic changes in the structures, frequencies, intensities and numbers of the absorption peaks [175]. This phenomenon is expected to be more significant in low-symmetry AAB-stacked and sliding bilayer graphene [65,66]. In sufficiently low magnetic fields, the spectral features reflect the band structures, such as the symmetry, energy dispersions and atomic interactions, as well as the broken mirror symmetry under the electric field.…”

“…The improved quality is adequate for research experiments and industrial applications [41][42][43][44][45][46][47][48][49]. In addition, AAB stacking and intermediate bilayer configurations, with relative layer-layer shifts or twists, have also been found and are becoming interesting subjects [59][60][61][62][63][64][65][66][67]. Synthesized graphene is generally comprised of different kinds of domain due to the tiny difference between the total energies of the different configurations.…”

“…AA [78][79][80], AB [81][82][83][84][85][86][87][88][89][90][91][92][93], ABC [93][94][95][96][97][98][99] and AAB [64], are predicted to display unique electronic energy dispersions. This new material holds great promise for the development of next-generation electronic and optoelectronic nanodevices [41-47, [50][51][52][53][54][55][56] because the electronic and optical properties can be flexibly tuned by the application of external fields [64][65][66][67][68][69][70][71][72][73][74] as well as changes to the geometric structures and dopants [115][116][117][118][119][120]…”