Dielectric Constant with Local Field Effects Included

The self-consistent field method of Cohen and Ehrenreich is used to obtain the macroscopic longitudinal dielectric constant that includes local field effects. The physical basis for the local field is discussed for nonlocalized electrons. In the limit of long wavelengths and low frequencies, it is shown that the dielectric constant can be split into an acceleration term that describes the motion of electrons from atom to atom and an atomic term that describes the motion of the electrons around each atom. It is proved that the acceleration term contains no local field correction whereas the atomic term does contain a local field correction. The local field correction is calculated explicitly for the weak binding limit and is found to be of the same order in the weak potential as the atomic term, but the coefficient is much smaller for most Fermi surfaces. This justifies, for most Fermi surfaces, the common practice of neglecting local field corrections. In the tight-binding limit, the Lorentz expression for the dielectric constant is obtained.