ASYMPTOTIC DISPLACED CHARGE ROUND IMPURITIES IN METAL CRYSTALS WITH AND WITHOUT SURFACES

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{variant}(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{variant} in the asymptotic region far from the defect. Provided V(r) has certain reasonable properties, it is shown that Δρ{variant} ~ 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. © 1979.