Width-engineered graphene nanoribbon reconfigurable intelligent surfaces with an optimal quantum-confinement window for terahertz 6G beam steering: a computational study

Reconfigurable intelligent surfaces are emerging as a means of shaping the propagation environment in terahertz wireless systems, yet the tunable elements available at these frequencies remain a limiting factor. Existing graphene metasurfaces treat the material as a continuous sheet whose only adjustable parameter is the gate-controlled chemical potential. The central novelty of this work is to introduce the graphene nanoribbon width, through its quantum-confinement bandgap, as an independent structural design parameter, and to show that there exists a finite window of ribbon width in which this confinement is beneficial for terahertz phase control rather than detrimental. This is examined through a computational model that couples a tight-binding band structure to the Kubo surface conductivity and a resonant reflective unit cell. The analysis reveals that the ribbon width controls the achievable phase range through the confinement gap: below roughly three nanometres the large gap removes the carriers responsible for the reactive conductivity and the reflection phase is largely frozen, whereas above this width the phase range rises and saturates at up to about 250 degrees for a single-layer cell, accompanied by monotonically decreasing loss. An optimal design window is identified in which the bandgap lies between approximately 0.30 and 0.50 electronvolts, corresponding to ribbon widths of about four to six nanometres, where the cell retains a wide phase range while suppressing residual absorption relative to a bulk-graphene reference. The conductivity model is verified against the analytic Drude limit, and the predicted single-layer phase range is benchmarked against published full-wave results for an equivalent graphene cell, with which it is quantitatively consistent. A parametric study across relaxation time and substrate thickness shows that the in-window cell retains lower loss than a bulk-graphene reference over the range of realistic graphene quality, while the operating band over which the cell holds a usable phase range and its stability under oblique incidence up to sixty degrees are both quantified. A sixteen-by-sixteen array constructed from in-window cells steers a beam to a prescribed direction with low sidelobe degradation, while a narrow, over-confined array suffers visible pattern distortion. The results identify ribbon width as a concrete design parameter for terahertz reconfigurable surfaces and quantify the window in which quantum confinement is beneficial rather than detrimental.