Band Structure and Lattice Distortion inV2O3

Abstract

A model for the band structure of a hexagonal (beehive) lattice in the tight-binding approximation is examined. The stability of the structure against distortions and the effects of distortions in splitting bands are investigated. The relationship of this model to the theory of Adler and Brooks for the metal-insulator transition of ${\mathrm{V}}_2$ ${\mathrm{O}}_3$ is discussed. It is shown that this model can account for a transition from a distorted, insulating state to an undistorted, semimetallic one, for certain values of the $d-d$ interaction integrals. The distortion does not double the size of the unit cell; therefore, the gap appears at the point k=0, rather than half way to the zone boundary.