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.
Part of the book: 2D Materials