Configuration-enriched magneto-electronic spectra of AAB-stacked trilayer graphene

Abstract

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.

Introduction

“…In the low-frequency region, rich optical excitation channels cause many absorption peaks, some of which show quasi-1D asymmetric divergence due to the vertical excitations between two constant energy loops. The LLs coming from the two valleys K and K′ are obviously separate in the mirror symmetry broken system [64]. The results present certain important differences for the state degeneracy, spacing, quantum number and spatial distribution of the wavefunctions, as compared with the highly symmetric configurations.…”

“…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].…”

“…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.…”

“…Few-layer graphene with specific stacking configurations, e.g. 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]…”

“…AAB-stacked graphene exhibits an extraordinary band structure compared to the AA, AB and ABC systems, mainly due to the low symmetry of its stacking geometry [64]. In the case of the trilayer system, AAB-stacked graphene is a narrow-gap semiconductor which presents a pair of subbands with strong oscillatory energy dispersions near = E 0 F .…”