Polarizability and Impurity Screening for Phosphorene

Using a tight-binding Hamiltonian for phosphorene, we have calculated the real part of the polarizability and the corresponding dielectric function, Re[ ϵ q ω ], at absolute zero temperature (T = 0 K) with free carrier density 10 13 / cm 2 . We present results showing Re[ ϵ q ω ] in different directions of the transferred momentum q. When q is larger than a particular value which is twice the Fermi momentum kF, Re[ ϵ q ω ] becomes strongly dependent on the direction of q . We also discuss the case at room temperature (T = 300 K). These results which are similar to those previously reported by other authors are then employed to determine the static shielding of an impurity in the vicinity of phosphorene.