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This paper provides a variational treatment of the effect of external chargeson the free charges in an infinite free-standing graphene sheet within theThomas-Fermi theory. We establish existence, uniqueness and regularity of theenergy minimizers corresponding to the free charge densities that screen theeffect of an external electrostatic potential at the neutrality point. For thepotential due to one or several off-layer point charges, we also provepositivity and a precise universal asymptotic decay rate for the screeningcharge density, as well as an exact charge cancellation by the graphene sheet.We also treat a simpler case of the non-zero background charge density andestablish similar results in that case.

Thomas-Fermi theory of out-of-plane charge screening in graphene