Electronic transport in order–disorder coupled bilayer graphene

Within the tight-binding framework, we investigate the electronic transport properties of AA- and AB-stacked ordered–disordered bilayer graphene using matrix diagonalization combined with the quantum diffusion theory, in the framework of a realistic materialized tight-binding Hamiltonian with long-range hopping. It is found that interlayer compression opens a bandgap, with the critical interlayer distance for gap opening being influenced by the disorder strength. As disorder increases, the electronic bands broaden, the density of states in the band tails remains low, while the band-center density stays high and stable, approaching the monolayer graphene band structure under strong disorder. Participation-number analysis indicates that all electronic states are nonlocalized under weak disorder, whereas mobility edges emerge under strong disorder, separating nonlocalized states in the band center from localized states in the band tails, and gradually blur as the interlayer distance decreases. Importantly, a universal anomalous quantum diffusion behavior is observed, regardless of interlayer compression, the electronic mobility undergoes a transition from decrease to increase with increasing disorder strength. By jointly tuning disorder strength and interlayer distance, the electronic diffusion can be effectively controlled between superdiffusive and subdiffusive regimes. Ordered–disordered bilayer graphene quantum films may be realized via doping, micro-/nano-fabrication, or substrate engineering. These results provide new theoretical insights into bilayer graphene and guidance for the design of novel electronic devices.