Tunable layer-specific polarizability in twisted multilayer graphene flakes capped with hexagonal boron nitride

Twisted multilayer graphene (TMG) capped with hexagonal boron nitride (hBN) exhibits distinctive electronic phenomena under a vertical electric field. However, the dielectric constant alone is insufficient to comprehensively characterize the dielectric properties of low-dimensional materials, posing challenges for accurately measuring and controlling their field response. To address this, we develop a site-specific polarizability decomposition approach based on first-principles calculations, enabling the separation of intra- and interlayer polarizabilities in TMG@hBN. This method is applied to 2580 constructed configurations of TMG flakes with and without hBN encapsulation. Our findings reveal that intralayer polarizability dominates the overall magnitude, while the interlayer component governs its variation with twist angle. hBN encapsulation enhances interlayer polarizability while reducing its twist-angle dependence. For both TMG and TMG@hBN, the inner graphene layers exhibit negligible γ, which quantifies the layer-specific interlayer charge transfer response to an external field, while significant γ values emerge in the outermost graphene layers (γGra) and hBN (γBN). Interestingly, γGra and γBN exhibit opposite signs in non-equivalent layers, and γGra reverses between pristine TMG and TMG@hBN. Compared to TMG, γGra in TMG@hBN is suppressed, with variations strongly dependent on thickness, twist angle, and stacking patterns, particularly when nitrogen atoms align over phenyl ring centers. In addition to the well-known Bernal-stacked structure, notable changes in interlayer polarizability and γGra are also observed in slightly misaligned (AA)N-stacked structures with the exceptional twist angle (θp). This scalable method enables layer-resolved analysis of intra- and interlayer contributions, offering new insights for tuning electric field responses and optimizing graphene-based optoelectronic devices.