@article {137116, title = {Electric-Field Dependence of the Effective Dielectric Constant in Graphene}, journal = {Nano Letters}, volume = {13}, year = {2013}, pages = {898-902}, abstract = {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 gatecontrolled 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-ofplane (Eext ⊥ ) and in-plane (Eext || ) 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 (Eext \< 0.01 V/{\r A}) 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.}, author = {Elton J. G. Santos and Efthimios Kaxiras} }