Bilayer graphene (BLG), as a two-dimensional crystalline form of carbon, with a controllable band gap, has been proposed as an alternative to graphene for nanoscale electronics. Through modeling single-electron transport in BLG, using Abelian group schemes Zm×Zm as a novel approach, the present paper has numerically studied metal-insulator transition using random matrix theory in doped AA-stacking BLG. In this mathematical technique, initially, Abelian group schemes and the underlying graph of honeycomb periodic lattice of the single-layer graphene were constructed. Then, the tight-binding Hamiltonian matrix of this layer was represented by the adjacency matrices of the graph. Through using these matrices, it is possible to generate m-dimensional Bose-Mesner algebra. Finally, by applying the wreath product of these matrices, the Hamiltonian was calculated. In fact, instead of the hopping integral between individual layers, the mathematical combination of their underlying graphs was considered. This would be generalized to more than two layers. Numerical results indicated that insulator to metal transition occurred at the threshold doping value C=0.5%, which has already been achieved. After this threshold value, by increasing doping, a fast quantum chaotic transition from Poisson to Wigner energy-level statistic distribution was observed. The paper has suggested that a sufficient difference in the concentration of dopant atoms at individual layers would be an efficient way of controlling metal-insulator transitions.

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graph random matrix theory graphs doped hopping integral crystalline form of carbon nanoscale electronics insulator to metal transition controllable band combination poisson to wigner energylevel statistic distribution modeling singleelectron transport in blg mdimensional bosemesner algebra finally adjacency matrices singlelayer graphene graph of honeycomb periodic lattice of quantum chaotic transition doping tightbinding hamiltonian matrix wreath product metalinsulator transitions abelian group schemes

R. HabibpourBisafar,S. Behnia, F. Rahimi,.Study the metal-insulator transitions of bilayer graphene: Abelian group schemes approach. 142 (),106498.

R. HabibpourBisafar,S. Behnia, F. Rahimi,"Study the metal-insulator transitions of bilayer graphene: Abelian group schemes approach" 142

R. HabibpourBisafar,S. Behnia, F. Rahimi,"Study the metal-insulator transitions of bilayer graphene: Abelian group schemes approach"