Electronic Properties of AB-Stacked Bilayer Graphene Nanoribbons with Zigzag and Armchair Orientations

The electronic properties of AB-stacked bilayer graphene nanoribbons (AB-BGNRs) with zigzag and armchair orientations are investigated in this study using a nearest-neighbour tight-binding (NNTB) approach combined with the non-equilibrium Green’s function (NEGF) method via MATLAB. To address the lack of clear and simple methodologies for solving energy-eigenvalue problems in AB-BGNRs, the final model is derived using justifiable simplifying assumptions, such as the application of basis functions, discretization of the Hamiltonian operator, and utilization of the plane wave approximation, all grounded in many-body theories and the modified Hartree simplification theory. The Hamiltonian matrices for both orientations are constructed with open boundary conditions to mimic real-world structures. Results show that zigzag-oriented AB-BGNRs exhibit metallic characteristics due to the absence of a bandgap, while armchair-oriented AB-BGNRs alternate between metallic and semiconducting properties. DOS analysis reveals an increase in degenerate low-energy states with increasing width for zigzag orientation and a lack of quantum states in the mid-band region for semiconducting armchair variants. This research contributes to our understanding of AB-BGNRs’ electronic characteristics and lays a foundation for future advancements in graphene-based electronic devices.