Stacking and edge dependent bandgap modulation in AA- and AB- stacked bilayer graphene nanoribbons induced by gate voltage

This paper investigates the effect of gate voltage on bandgap modulation in bilayer graphene nanoribbons (BGNRs) with AA and AB stacking configurations, considering both zigzag and armchair edge geometries. Using a direct k-space diagonalisation approach applied to the nearest-neighbour tight-binding (NNTB) Hamiltonian, the study systematically examines electronic properties across a broad parameter space defined by stacking order, edge type, ribbon width classified by unit cells and gate voltages up to 2 eV. The applied gate voltage generates an electric field that breaks inversion symmetry, enabling controlled bandgap tuning. Results reveal distinct stacking- and edge-dependent properties: zigzag AA-BGNRs show minimal bandgap variation, whereas zigzag AB-BGNRs exhibit significant, nearly linear bandgap modulation under gate voltage. For armchair BGNRs, the electronic response varies with ribbon width families (3n, 3n + 1, 3n + 2) and stacking type. Notably, the 3n and 3n + 2 families remain semiconducting at zero bias, with the 3n family presenting the largest intrinsic bandgaps (~ 0.6 eV for AA, ~ 1.3 eV for AB) and distinct gate-induced modulation. The 3n + 1 family, metallic in AA stacking regardless of gate voltage, undergoes a metal-to-semiconductor transition in AB stacking, with the bandgap opening and increasing as gate voltage rises. This comprehensive analysis provides quantitative insights into intrinsic and tunable bandgaps, establishing a unified framework for understanding stacking- and width-dependent electronic properties in BGNRs. The findings offer valuable design guidelines for gate-tunable nanoelectronic and optoelectronic devices, including field-effect transistors and reconfigurable circuits, by linking electronic properties directly to ribbon structural parameters.