Regular Article

Electronic properties of slid bilayer graphene: effective models in low energy range

¹ National University of Civil Engineering (NUCE), 55 Giai Phong road, Hanoi 10000, Vietnam
² Phenikaa Institute for Advanced Study (PIAS), Phenikaa University, Yen Nghia ward, Ha Dong district, Hanoi 10000, Vietnam

^a e-mail: tahs@nuce.edu.vn
^b e-mail: nam.dovan@phenikaa-uni.edu.vn

Received: 30 June 2020
Received in final form: 8 August 2020
Accepted: 24 August 2020
Published online: 5 October 2020

Abstract

A generic tight-binding model for 2p_z 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.