Dual-gated self-referenced C₄-symmetric graphene metasurface for multiband terahertz refractive-index sensing

Graphene metasurfaces provide an electrically tunable platform for terahertz (THz) sensing; however, drift in the graphene electronic state can produce resonance shifts that are difficult to distinguish from analyte-induced changes. Here, we propose a dual-gated, C₄-symmetric graphene metasurface comprising a split-octagonal ring and a clover-disk resonator separated by hexagonal boron nitride (hBN). The numerical framework yields six resonances from approximately 0.78 to 2.62 THz, bulk refractive-index (RI) sensitivities of 0.119-1.162 THz RIU^-1, and figures of merit of 4.81-23.69 RIU^-1. Modes 1 and 6 respond differently to RI loading and common chemical-potential variation, enabling two-mode self-referencing. For common drift of ±0.06 eV and 1 GHz readout noise, the model predicts a reduction in RI root-mean-square error from approximately 6.48 × 10^-2 to 4.63 × 10^-3 RIU. Full-wave rigorous coupled-wave analysis surface-current maps further indicate interlayer coupling and increasingly distributed hybridization at the higher-frequency resonances. These results establish a testable strategy for exploiting electrically distinguishable graphene modes in multiband sensing with common-mode electronic-drift rejection.