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Using a tight-binding Hamiltonian for phosphorene, we have calculated thereal part of the polarizability and the corresponding dielectric function,Re$[\epsilon(\textbf{q},\omega)]$, at zero temperature (T = 0) with freecarrier density $10^{13}$/ $cm^2$. We present results showing the real part ofdielectric function in different directions of the transferred momentum$\bf{q}$. When $q$ is larger than a particular value which is twice the Fermimomentum $k_F$, Re$[\epsilon(\textbf{q},\omega)]$ becomes strongly dependent onthe direction of $\bf{q}$. We also discuss the case at room temperature (T =300K). These results which are similar to those previously reported by otherauthors are then employed to determine the static shielding of an impurity inthe vicinity of phosphorene.

Polarizability and impurity screening for phosphorene