Application of the excitonic model to the metal-insulator transition of a simple band model

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Abstract
The electronic structure of a system resembling the insulating state of V2O3, at zero temperature, is calculated, making use of the excitonic formalism. The calculation is based on a previous band-structure calculation, by the tight-binding method, and on the assumption of intra-atomic Coulomb interaction. It is shown that several insulating states exist which possess an energy lower than that of the semi-metallic (or metallic) state, which is lowest in energy when the Coulomb interaction is neglected. These excitonic states possess the features characteristic of the insulating state of V2O3, namely magnetic order and/or lattice distortion. It is shown that the force driving the metal to insulator transition is the tendency of the electrons to localize, as suggested by Mott, but the localization of the electrons on the atoms is only partial, and therefore the energy gap in the insulating state is small compared with the Coulomb energy and with the width of the 3d band. Also, it is shown that the localization of the electrons is associated with a breakdown of the symmetry of the electronic ground state. The symmetry of the wave-functions of the semi-metallic state is shown to play a vital role in determining the nature of the transition. This calculation, though it does not apply quantitatively to V2O3, possesses elements giving a qualitative and perhaps semi-quantitative description of features associated with this, and perhaps some other metal to insulator transitions.

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