Electronic properties of slid bilayer graphene: effective models in low energy range
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THE EUROPEAN PHYSICAL JOURNAL B
Regular Article
Electronic properties of slid bilayer graphene: effective models in low energy range Sy-Ta Ho 1,a , Hoang Anh Le 2 , Van Duy Nguyen 2 , and Van-Nam Do 2,b 1 2
National University of Civil Engineering (NUCE), 55 Giai Phong road, Hanoi 10000, Vietnam Phenikaa Institute for Advanced Study (PIAS), Phenikaa University, Yen Nghia ward, Ha Dong district, Hanoi 10000, Vietnam Received 30 June 2020 / Received in final form 8 August 2020 / Accepted 24 August 2020 Published online 5 October 2020 c EDP Sciences / Societ`
a Italiana di Fisica / Springer-Verlag GmbH Germany, part of Springer Nature, 2020 Abstract. A generic tight-binding model for 2pz electrons in bilayer graphene (BLG) systems is used to derive the expression of effective Hamiltonians for low-energy states around the K-points of hexagonal Brillouin zone. The obtained effective Hamiltonians are validated for two kinds of AA-like and AB-like slid bilayer graphene (SBG). It is shown that, for the former case, the electronic structure is characterized by a gauge vector field which couples to the sliding vector to deform the band structure of the AA-stacked configuration as a perturbation. For the latter case, since the A–B interlayer coupling is the most dominant, it allows separating the energy bands and lowering the 4 × 4 Hamiltonian into a 2 × 2 effective model. A gauge vector field also appears, but different from the AA-like SBGs, it plays the role similar to an in-plane magnetic field.
1 Introduction Hetero-structuring is a way to modulate the electronic structure of resulted material systems. Similarly, it was experimentally demonstrated that stacking twodimensional (2D) material layers allow engineering the electronic structure of 2D systems [1–5]. Graphite flakes can be seen as the natural stacking of few layers of graphene (FLG). Bilayer graphene (BLG) is the simplest few-layer graphene system (FLG) in which the van der Waals interaction plays the role of binding two graphene layers. In the FLGs, graphene layers preferably stack in the AB [6,7] and ABC [8] patterns. For the BLGs, it was shown that the two graphene layers can identically stack together, forming the so-called AA-stacked configuration, apart from the AB-stacked one [9]. The electronic structure of the AA- and AB-stacked configurations are different [10]. It is because of their different lattice symmetries that govern the coupling of electronic states in the two graphene layers. Though both configurations have the same translational symmetry, their point groups are D6h and D3 for the AA- and AB-stacked lattices, respectively. Consequently, the ABstacked configuration shows the electronic structure in the momentum space as the two couples of separate parabolic surfaces with the touching of one up and one down at a b
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the corner K-points of the Brillouin zone. Meanwhile, the band structure of the AA-stacked configuration can be seen as the interlocking of two pairs of Dirac cones
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