Flores, F; March, NH; Ohmura, Y; Stoneham, A; (1979) Asymptotic displaced charge round impurities in metal crystals with and without surfaces. Journal of Physics and Chemistry of Solids , 40 (7) 531 - 537. 10.1016/0022-3697(79)90081-7.

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Abstract

The displaced charge Δρ at distance r from a localized perturbation V in an inhomogeneous degenerate electron gas may be written in a linear response framework as Δϱ(r) = ∝V(r′)F(rr′)dr′. The response function F is expressed in terms of the Green function of the unperturbed system and attention is then focussed on two cases: * 1. o| * 2. (i) A perfect periodic metal crystal, perturbed by V. * 3. (ii) A metal lattice with a surface in which V is embedded. A full discussion is given of the influence of Fermi surface topology on the anisotropy of Δϱ in the asymptotic region far from the defect. Provided V(r) has certain reasonable properties, it is shown that Δϱ ~ r−nx oscillatory function. For the bulk metal, n can take values between 1 and 5 in different directions for Fermi surfaces with particular topologies. Possible experiments which bear on this anisotropy are briefly referred to. For a planar surface, the displaced charge is shorter range for V embedded in the surface than for the bulk metal, in most, but not all cases. For a closed Fermi surface with non-zero curvature, n = 5 for the parallel configuration.

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