Lindhard theory

Lindhard theory is a method of calculating the effects of electric field screening by electrons in a solid. It is based on quantum mechanics (first-order perturbation theory) and the random phase approximation.

Thomas–Fermi screening can be derived as a special case of the more general Lindhard formula. In particular, Thomas–Fermi screening is the limit of the Lindhard formula when the wavevector (the reciprocal of the length-scale of interest) is much smaller than the fermi wavevector, i.e. the long-distance limit.

This article uses cgs-Gaussian units.

The Lindhard formula for the longitudinal dielectric function is given by

Here, ${\displaystyle V_{q}}$ is ${\displaystyle V_{eff}(q)-V_{ind}(q)}$ and ${\displaystyle f_{k}}$ is the carrier distribution function which is the Fermi–Dirac distribution function (see also Fermi–Dirac statistics) for electrons in thermodynamic equilibrium. However this Lindhard formula is valid also for nonequilibrium distribution functions.

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