Thickness and Stacking Dependent Polarizability and Dielectric Constant of Graphene–Hexagonal Boron Nitride Composite Stacks

Abstract

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 (∼0.1 V/A), although the relative permittivity (er) of a composite stack increases with the number of layers, er for a fixed stack thickness is independent of the field strength. However, at higher electric field strength, er 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 th...