Electric-field dependence of the effective dielectric constant in graphene

The dielectric constant of a material is one of the fundamental features used to characterize its electrostatic properties such as capacitance, charge screening, and energy storage capability. Graphene is a material with unique behavior due to its gapless electronic structure and linear dispersion near the Fermi level, which can lead to a tunable band gap in bilayer and trilayer graphene, a superconducting-insulating transition in hybrid systems driven by electric fields, and gate-controlled surface plasmons. All of these results suggest a strong interplay between graphene properties and external electric fields. Here we address the issue of the effective dielectric constant (ε) in N-layer graphene subjected to out-of-plane (E(ext)(⊥)) and in-plane (E(ext)(||)) external electric fields. The value of ε has attracted interest due to contradictory reports from theoretical and experimental studies. Through extensive first-principles electronic structure calculations, including van der Waals interactions, we show that both the out-of-plane (ε(⊥)) and the in-plane (ε(||)) dielectric constants depend on the value of applied field. For example, ε(⊥) and ε(||) are nearly constant (~3 and ~1.8, respectively) at low fields (E(ext) < 0.01 V/Å) but increase at higher fields to values that are dependent on the system size. The increase of the external field perpendicular to the graphene layers beyond a critical value can drive the system to a unstable state where the graphene layers are decoupled and can be easily separated. The observed dependence of ε(⊥) and ε(||) on the external field is due to charge polarization driven by the bias. Our results point to a promising way of understanding and controlling the screening properties of few-layer graphene through external electric fields.