ISSN - 00319007, EISSN - 10797114, Physical Review Letters, 2008, vol. 100, p. -
Screening of coulomb impurities in graphene
We calculate exactly the vacuum polarization charge density in the field of a subcritical Coulomb impurity, Z|e|/r, in graphene. Our analysis is based on the exact electron Green's function, obtained by using the operator method, and leads to results that are exact in the parameter Zα, where α is the "fine-structure constant" of graphene. 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 Zeff, determined by the localized induced charge. We find that an impurity with bare charge Z=1 remains subcritical, Zeffα<1/2, for any α, while impurities with Z=2, 3 and higher can become supercritical at certain values of α. © 2008 The American Physical Society.