On the propagation of electron screening in disordered conductors

In condensed matter theories within the nonrelativistic framework, the screening of electrons in a free space takes place instantaneously, i.e., at infinite speed. In this paper, considering the screening in disordered (or random) systems, we show that it propagates at a finite speed of (ℓ/λ)ℓ/τ, depending on a ratio ℓ/λ of the electron mean free path ℓ and screening length λ, where ℓ/τ is the propagation speed of electrons between impurity potentials, which is identical to the Fermi velocity, and τ the electron elastic scattering time, thereby indicating that if the condition ℓ⪢λ holds like a situation in ordinary dirty conductors, the influence of retardation on the screening can be ignored safely in the same theoretical framework as above.