Study the metal-insulator transitions of bilayer graphene: Abelian group schemes approach. (June 2020) - Behnia, S.; HabibpourBisafar, R.; Rahimi, F.
Abstract: 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 Z m × Z m 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. Highlights: A new mathematical method based on Abelian group schemes for analyzing bilayer graphene properties is proposed. The Tight-binding Hamiltonian matrix of each layer is represented by the adjacency matrices of the Cayley graph. The complex geometrical lattice structure as an essential challenge in calculations has been removed. By using numerical analysis of eigenvalues, we investigate on the M-I transitions of bilayer graphene. This model can be generalized to other materials with different geometrical lattices.