Short-range Coulomb screening in a dielectric crystal

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Abstract
We study the near dielectric screening of the Coulomb repulsion by a lattice of point polarizable elements. We find that the far screening factor (related to the static dielectric constant) persists even to distances of one or two lattice spacings. In some configurations the screening factor is enhanced by proximity, and we exhibit a case (two like charges at body-centered positions one spacing apart in a simple-cubic lattice) in which the screening factor exceeds 1 by ∼1%, although the polarizability is still below the Luttinger antiferroelectric threshold. Thus the dielectric screening overcomes the bare Coulomb repulsion in this case, and the net effect is attractive. Such considerations may play a part in explaining the mechanism of short-range pairing in cuprate superconductors. Incidentally we demonstrate that for the NaCl type of crystal there exists a small range of ratios of ionic polarizability for which a third configuration is preferred at T=0 K to both the ferroelectric and the Luttinger antiferroelectric spontaneous polarization.