Group-Theoretical Treatment of the Energy Bands in Metal Borides MeB₆

Abstract

The tight-binding approximation is applied to a study of electronic energy bands in metal borides MeB₆. The 25×25 determinantal secular equation for the energy is reduced by a group-theoretical treatment of the spatial symmetry at certain special values of the wave vector K. The results are that if metal atoms have two valence electrons the valence bands are all filled and the conduction bands are all empty, and in the case of calcium boride CaB₆ the narrowest gap between valence-and conduction-bands is at edges of the first Brillouin zone, the simple cube in the reciprocal space and its width is about 1.5 eV, in good agreement with empirical results that there exist only borides of elements having two valence s electrons in this type of structure.