As a check, make sure your result reverts the bare Coulomb potential if ge → 0 For a metal with a density n 1028 m and a Fermi energy E, ~3eV estimate the Thomas Fermi screening length (Te = V/e²gf (given here in SI units). Complete the calculation by carrying out the Fourier integrals for the case of a point charge Q embedded in a degenerate electron gas with a density of states at the Fermi energy (per unit volume) gf to derive the form of its screened real space potential. The setup for this calculation is given in Pencast 8. It is based on the assumption that the electrons in a many electron atom feel a constant potential over their wavelength and, thus, may be approximated by a local plane wave. the ionization energy and the polarizability. Since the Coulomb potential produced by a modulated charge profile Pext(q) in Fourier space is 4 Vext (9) - Pext (9) q? the Thomas Fermi model gives us the self-consistently screened potential 41 Pext (9) Vse(9) q? +4ne We want an explicit form for this potential sourced by a point charge Q. Thomas and Fermi and allows for the calculation of some simple properties of many electron atoms and ions, e.g. sion in the two cases, the density of states is linear constant in SLG BLG, leading to very distinct screening behavior in the two cases:9,10 q TF SLG k F q TF BLG k F 0 constant, where q is the long wavelength Thomas-Fermi screening wave vector and k F n is the Fermi wave vector with n as the tunable 2D carrier density. Transcribed image text: In the Thomas Fermi model the q-th Fourier component of an external static charge density Pext is screened by a static q-dependent dielectric constant given by 4πε?gr (q) = 1 + q? where gf is the density of states at the Fermi energy.
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