Screening of Coulomb Impurities in Graphene

Abstract

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 $Z\alpha$, where $\alpha$ 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 $Z_{eff}$, determined by the localized induced charge. We find that an impurity with bare charge Z=1 remains subcritical, $Z_{eff}\alpha <1/2$, for any $\alpha$, while impurities with $Z=2,3$ and higher can become supercritical at certain values of $\alpha$.

4 pages, 2 figures

References in corpus (12)

• Electric Field Effect in Atomically Thin Carbon Films
• Unconventional quantum Hall effect and Berry's phase of 2pi in bilayer graphene
• Carrier transport in 2D graphene layers
• Strong suppression of weak (anti)localization in graphene
• Landau Level Splitting in Graphene in High Magnetic Fields
• Quantum transport of massless Dirac fermions in graphene
• The Coulomb impurity problem in graphene
• Vacuum Polarization and Screening of Supercritical Impurities in Graphene
• Nonlinear screening of charge impurities in graphene
• Screening of a hypercritical charge in graphene
• Coulomb impurity in graphene
• Theory of quantum impurities in spin liquids

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