Thickness and electric-field-dependent polarizability and dielectric constant in phosphorene

Based on extensive first-principles calculations, we explore the thickness-dependent effective dielectric constant and slab polarizability of few-layer black phosphorene. We find that the dielectric constant in ultrathin phosphorene is thickness-dependent and it can be further tuned by applying an out-of-plane electric field. The decreasing dielectric constant with reducing number of layers of phosphorene is a direct consequence of the lower permittivity of the outer layers and the increasing surface-to-volume ratio. We also show that the slab polarizability depends linearly on the number of layers, implying a nearly constant polarizability per phosphorus atom. Our calculation of the thickness-and electric-field-dependent dielectric properties will be useful for designing and interpreting transport experiments in gated phosphorene devices, wherever electrostatic effects such as capacitance and charge screening are important.