Lower (negative) bounds on the static electric susceptibility of non-equilibrium cubic crystals

We use a classical, microscopic model of point-like dipolarizable entities (a model that is standard in the case of positive polarizability) and investigate its behavior for simple cubic (sc), body-centered cubic (bcc), and face-centered cubic (fcc) crystals with one entity per primitive cell when the static polarizability of the entities is negative and the mutual interaction between the entities is taken into account. We find that the static electric susceptibility is bounded below due to an instability towards self-polarization but the lower permissible bound is negative definite in each case, i.e., the concept of negative static electric susceptibility remains robust, according to the model, when mutual interactions are taken into account. The usual Clausius-Mossotti relation between the static polarizability and the static electric susceptibility remains valid in the case of negative parameters, but only down to the lower permissible bound; the value of the bound depends on the crystal structure and is always unrelated to the asymptote of the Clausius-Mossotti curve. The lower permissible bounds of the static electric susceptibility are found to be -0.906 for sc, and -1.00 for bcc and fcc. These results confirm that, although the magnitude of the static electric susceptibility does not diverge in the negative case (as it can in the positive case), the magnitudes attainable in the negative case for condensed media may, nevertheless, be many orders of magnitude greater than those predicted previously for inverted vapors and gases. This is a promising result in relation to the development of potential new technologies that exploit the phenomenon.