Dynamically tunable and ultrastable plasmonic bound states in the continuum in bilayer graphene metagratings

Bound states in the continuum (BICs), a universal wave phenomenon observed in plasmonic and other wave systems, remain spatially localized despite coexisting with a radiative continuum. However, current implementations of plasmonic BICs (pBICs) suffer from critical limitations: lack of dynamic tunability or poor stability in key parameters such as resonance wavelengths and quality factors (Q factors). In this paper, we propose a bilayer graphene metagrating with sinusoidal periodic conductivity modulation to address these challenges. We demonstrate two independent pBICs with quantized topological charge (\ensuremath{-}1, confirmed via momentum-space polarization singularities), emerging under in-phase and out-of-phase conductivity configurations. Remarkably, owing to the invariant coupling strength under arbitrary lateral offsets of interlayer conductivity patterns, these pBICs exhibit ultralow variance in both wavelengths and Q factors within a particular range of asymmetry parameters, ensuring unprecedented spectral stability under perturbations. The proposed metagrating architecture enables high-performance refractive index sensing and dual-mode perfect absorption, offering a robust platform for actively tunable pBIC devices with tailored spectral and topological functionalities.