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 (epsilon) in N-layer graphene subjected to out-of-plane (E-ext(perpendicular to)) and in-plane (E-ext(parallel to)) external electric fields. The value of epsilon 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 (epsilon(perpendicular to)) and the in-plane (epsilon(parallel to)) dielectric constants depend on the value of applied field. For example, epsilon(perpendicular to) and epsilon(parallel to) are nearly constant (similar to 3 and similar to 1.8, respectively) at low fields (E-ext < 0.01 V/angstrom) 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 epsilon(perpendicular to) and epsilon(parallel to) 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.