Role of small polarons in the metal-insulator transition

Abstract

An analysis of the effects of small polaron formation on the metal‐insulator transition as expressed in terms of the Hubbard model is presented. The system dealt with contains an electronic subsystem and a rigid lattice of polarizable molecules. The electron‐excitation coupling is treated by a canonical transformation that leads to reduced Hubbard constants for both the Coulomb interaction and the bandwidth. Polaron formation leads in addition to the creation of a polarization bond in the crystal. This contribution to the total cohesive energy of the solid is shown to be equal in magnitude to the polaron binding energy. The effective antiferromagnetic exchange interaction (via virtual charge transfer) is calculated for both excitonic and phononic polarons. A discussion of the effect of increased polarizability is presented with emphasis on the possibility of stabilizing the metallic phase at low temperatures in real crystals.