Temperature Effect on the Static Polarization of Monolayer and Bilayer Phosphorus

The polarizability of monolayer and bilayer phosphorus is calculated. Results will be presented at various temperatures as well as when a vertical electric field is applied. We employ our polarization function in calculating the static shielded potential of a nonmagnetic impurity in its vicinity. We also investigate the way in which this static shielding is modified for a scaffold structure involving a thick conductor forming a substrate for the phosphorus layers. Our calculations make use of the inverse dielectric function which we obtain in the random-phase approximation. We also report on our calculations when the impurity distance from the conductor surface or 2D layer is varied.