Coulomb Impurity Screening in Graphene

I will discuss the vacuum polarization charge density around a Coulomb impurity with charge $Z|e|$. Perturbation theory in powers of $Z\alpha$ (where $\alpha = e^{2}/v_{F}$ is the effective coupling constant in graphene), shows that the polarization charge is localized at the impurity site. An exact calculation, based on the Green's function in a Coulomb field, leads to a non-perturbative result, valid to all orders in $Z\alpha$ [1]. Taking into account also electron-electron interactions in the Hartree approximation, we solve the problem self-consistently in the subcritical regime, where the impurity has an effective charge $Z_{\mbox{eff}}$, determined by the localized induced charge. We find that an impurity with bare charge $Z=1$ remains subcritical, $Z_{\mbox{eff}} \alpha < 1/2$, for any $\alpha$, while impurities with $Z=2,3$ and higher can become supercritical at certain values of $\alpha$. \newline [1] I.S. Terekhov, A.I. Milstein, V.N. Kotov, and O.P. Sushkov, arXiv:0708.4263.