Abstract
Rigorous formulas are derived for the nonlocal transverse and longitudinal conductivities and dielectric functions of a free electron gas in the presence of isotropic impurity scattering. The results are valid for h ̷ ω ⪡ μ, k Fl ⪢ 1 , and arbitrary values of q. By comparing the results with those derived from the Boltzmann equation method and the Lindhard dielectric functions we establish that the former is valid for q ⪡ k F and the latter for q ≳ k F . At low frequencies (ωτ ⪡ 1) there is a range of q where both Boltzmann and Lindhard formulas break down, and at high frequencies (ωτ ⪢ 1) the two formulas overlap for a range of q. The effects of scattering anisotropy are also examined, and it is found that the dominant effect can be accounted for by replacing the scattering time in the isotropic scattering model by the relaxation time for transport.
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