ABSTRACT
When a metal is subjected to a static but spatially slowly varying external charge density, we found in Sec. 6.1 that the conduction electrons screen this perturbation beyond λ TF $ \lambda_{TF} $ https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9781351121996/259a876e-1ad1-4598-839f-e9587e88d783/content/inline-math10_1.tif"/> , the Thomas-Fermi screening length. Since the electric field E in this case is purely determined by the Poisson law, ∇ ⋅ E = - ρ/ɛ 0, it is purely longitudinal, or, curl-free. Thus, purely longitudinal electric fields get screened by the conduction electrons. A magnetic field B is in contrast purely transverse (divergence-free), and a static magnetic field is in fact not screened by the conduction electrons. When the electromagnetic fields are time-dependent, apart from the magnetic field which is always transverse, the electric field may also acquire a transverse component. In Sec. 6.7, it was shown that time-dependent magnetic fields are screened beyond the skin depth λ skin = 1 / σ μ μ 0 ω $ \lambda_{skin} = 1/\sqrt {\sigma \mu \mu_{0} \omega } $ https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9781351121996/259a876e-1ad1-4598-839f-e9587e88d783/content/inline-math10_2.tif"/> , with σ the conductivity, μ the magnetic permittivity and μ 0 the permittivity of vacuum. The lack of screening of transverse fluctuations of the electromagnetic fields in a metal indicates in turn strong effects on the electronic properties. Some of these effects will be discussed here.
