▎ 摘　　要

The giant carrier mobility of graphene is significantly reduced due to external perturbations, such as substrate based charge impurities, and their impact can be minimized by encapsulating graphene between hexagonal boron nitride (hBN) layers. Using density functional theory (DFT) based ab initio calculations, we study the static response of such a composite by placing it in a vertical electric field. We find that at relatively low electric field (similar to 0.1 V/angstrom), although the relative permittivity (epsilon(r)) of a composite stack increases with the number of layers, 8, for a fixed stack thickness is independent of the field strength. However, at higher electric field strength, epsilon(r) increases monotonically with the applied field strength even for a fixed stack thickness, signifying nonlinear response. The relative permittivity changes more readily for graphene rich stacks as compared to hBN rich stacks, which is consistent with the property of the pristine phases. We also present an empirical formulation to calculate the thickness and stacking dependent effective dielectric constant of any arbitrary stack of graphene-hBN layers, which fits very well with the ab initio calculations. Our empirical formulation will also be applicable for van der Waals stacks of other two-dimensional materials and will be useful for designing and interpreting transport experiments, where electrostatic effects such as capacitance and charge screening are important.