The Induced Charge Generated By The Potential Well In Graphene

TL;DR

This paper analyzes the induced charge density in graphene caused by a finite potential well, deriving explicit expressions for large distances and different regimes using Green's function methods.

Contribution

It provides a detailed theoretical derivation of induced charge distributions in graphene due to a potential well, including subcritical and supercritical regimes.

Findings

Derived expressions for induced charge density at large distances.

Analyzed induced charges inside and outside the potential well.

Applied Green's function approach for the calculations.

Abstract

The induced charge density, $\rho_{ind}(\bm r)$, generated in graphene by the potential well of the finite radius $R$ is considered. The result for $\rho_{ind}(\bm r)$ is derived for large distances $r\gg R$. We also obtained the induced charges outside of the radius $r\gg R$ and inside of this radius for subcritical and supercritical regimes. The consideration is based on the convenient representation of the induced charge density via the Green's function of electron in the field.