Lower negative bounds on the static electric susceptibility of nonequilibrium cubic crystals

We use a classical, microscopic model of pointlike 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 electrostatic 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 negative values are possible in each case. The usual Clausius-Mossotti relation between the static polarizability and the static electric susceptibility remains valid in the case of negative parameters but is truncated at the lower 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 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.