Thomas-Fermi Screening in Graphene

The in-plane static screening of the field originated by a charge placed in a graphene sheet is investigated. A self-consistent field equation in the real space domain is obtained by using a suitable Thomas-Fermi procedure. Exact and approximated (for qualitative considerations) solutions are presented. In the case of a charged sheet, the screened potential presents a tail dependent on the free carrier density whose importance is connected with the local features of the impurity system. Early conclusions about Thomas-Fermi screening in graphene are revised. PACS: 71.10.Ca, 73.61.Le Graphene is a bidimensional structure which has newly attracted the interest of physic community since the recent report on the successful isolation of free-standing carbon monolayers [1]. The striking properties of this material ensue from the peculiar electronic structure which in the ideal honeycomb lattice shows gapless (approximately) linear-spectrum bands with degeneracy points (two per cell) at the corners of the hexagonal Brillouin zone [2]. Due to a peculiar suppression of localization effects, electrical conductivity never falls below a certain value (resistivity ρmax ≈ 6.5 kΩ) corresponding to the quantum unit of Mott conductance [1]. Anomalous effects in transport properties were successfully explained in the framework of the quantum electrodynamics [3] which idealize the electron spectrum (near the two degeneracy points) as the one of a 2D-gas of massless two-fermion-Dirac quasiparticles [4]. Carrier populations can be changed by thermal excitation or/and by electrically induced band shift. Electron or holes are poured into bands in order to match the equilibrium Fermi level. Accordingly, electron or hole conductivities can be settled by applying suitable gate voltages [1]. This paper is devoted to the investigation of the static screening properties in the gapless bidimensional semiconductor. Really, screening in bidimensional electron gas was already investigated by using the self-consistent-field dielectric formulation of Ehrenreich and Cohen (EC) [5]. According to the EC’s work, involved in 3D electron gas, the self consistency can be attained by combining the single-particle Liouville and the Poisson equations [6], thus allowing for the Lindhard longitudinal dielectric constant [7]. The repetition of this procedure in a 2D system [5] may be questioned since it lacks a proper handling of Poisson equation for the confined electron gas. A different approach, still based on the EC’s work, was addressed to investigate static screening in graphite layers