Induced Charge Generated by Potential Well in Transition Metal Dichalcogenides

Abstract—We investigate the asymptotic behavior of the charge density ρ_ind(r) induced by an azimuthally symmetric potential well of finite radius R. The analytic expression for ρ_ind(r) at the distances r $ \gg $ R is obtained. It is shown that, for a wide range of potential parameters, the induced charge density can be represented as ρ_ind(r) = F(r)${{\mathcal{L}}_{V}}$, where F(r) depends only on distance and ${{\mathcal{L}}_{V}}$ depends on the parameters of the potential. We also investigate the behavior of the induced charge density when the potential well depth close to the critical value.