  Black phosphorus (BP), a layered van der Waals (vdW) crystal, has unique
in-plane band anisotropy and many resulting anisotropy properties such as the
effective mass, electron mobility, optical absorption, thermal conductivity and
plasmonic dispersion. However, whether anisotropic or isotropic charge
screening exist in BP remains a controversial issue. Based on first-principles
calculations, we study the screening properties in both of single-layer and
bulk BP, especially concerning the role of doping. Without charge doping, the
single-layer and bulk-phase BP show slight anisotropic screening. Electron and
hole doping can increase the charge screening of BP and significantly change
the relative static dielectric tensor elements along two different in-plane
directions. We further study the charge density change induced by potassium (K)
adatom near the BP surface, under different levels of charge doping. The
calculated two-dimensional (2D) charge redistribution patterns also confirm
that doping can greatly affect the screening feature and tip the balance
between isotropic and anisotropic screening. We corroborate that screening in
BP exhibit slight intrinsic anisotropy and doping has significant influence on
its screening property.
