Metallic Transitions in Ionic Crystals: Some Group Theoretical Results

Abstract

In view of a discrepancy between results available in the literature, the problem of finding the different irreducible representations for points on the surface of the Brillouin zone in NaCl and CsCl type lattices is re-examined for particular points of high symmetry. The lattice harmonics to be included in cellular-type calculations are listed up to and including $l=10\mathrm{}$ for two points on the surface of the Brillouin zone in each case. Our results confirm the earlier work of Bell up to $l=6\mathrm{}$, and extend her tables somewhat. The present findings however are at variance with Behringer's work on LiH for one of the points ($W$) which he considers.