Polarizability and impurity screening for phosphorene

Abstract

Using a tight-binding Hamiltonian for phosphorene, we have calculated the real part of the polarizability and the corresponding dielectric function, Re$[\epsilon (\text{q},\omega )]$, at zero temperature (T = 0) with free carrier density $10^{13}$/ $c{m}^2$. We present results showing the real part of dielectric function in different directions of the transferred momentum $\mathbf{q}$. When $q$ is larger than a particular value which is twice the Fermi momentum $k_F$, Re$[\epsilon (\text{q},\omega )]$ becomes strongly dependent on the direction of $\mathbf{q}$. We also discuss the case at room temperature (T = 300K). 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.