The Induced Charge Generated By The Potential Well In Graphene

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.
Comment: 12 pages, 2 figures, version published in Phys.Rev. B