Thermodynamic Analysis of Metal-Insulator Transitions. Effect of Changes in the Density of States Function

Abstract

Prior theories of metal-insulator transitions by Spa lek et al. were extended to include quartic terms in the temperature and by introducing two different density of state functions. The effects of these extensions on low-temperature metal-insulator transitions and on reentrant metallic behavior in solids have been investigated. PACS numbers: 71.10. Hf, 71.10.Ay, 71.30.+h, 71.45.Gm PreliminariesThere has been continuing interest in the proper treatment of metal-insulator transitions in general, and in the special situation where one encounters reentrant metallic behavior. This is manifested, for example, in the electrical properties of paramagnetic V 2 O 3 doped with small amounts of Cr. With rising temperature T above 180 K, one first observes metallic characteristics; followed by a first-order transition to an insulating state; followed at still higher temperatures by another transition back to the metallic regime [1]. Also, there are instances, such as the NiS 2−y Se y system, that exhibit a metal-insulator transition with rising temperature close to absolute zero [2]; the latter runs contrary to normal observations of an insulator-metal transition with rising T . These unusual situations have been rationalized lately by invoking the dynamic mean field theoretical approach, as championed by a number of research groups [3]. Their principal aim was to generate partial density-of-states curves which match experimental photoemission results, and to note changes concomitant to the occurrence of the metal-insulator transition. While their success is certainly impressive, the theoretical analysis requires considerable computational expertise, such that the fundamentals operative in forcing the electronic changes are not readily discerned. This invites a retrospection to earlier work, beginning with the discussions by Mott This included a procedure originally proposed by Spa lek and co-workers [6-8] who developed more elementary approach on which the subsequent discussion of this article is based. They considered an assembly of interacting electrons in a solid as a collection of independent quasiparticles that are subject to the framework of solid state physics. In the simplest case, one deals with nondegenerate band that is exactly half-filled, and for which -in the insulating state at the zero of temperature -each of the N lattice sites is occupied by one electron. At nonzero temperatures any given lattice site may be empty, accommodate one electron of either spin, or two electrons with paired spins. Double occupancies are energetically disfavored by the Coulomb repulsion U between the two electrons on the same site; electron interactions between more distant neighbors are ignored. Let η represent the probability of encountering a given lattice site in a doubly occupied configuration. Then the total repulsive energy is specified by NUη. Relative to this state, the mobile electrons have an average negative kinetic energyε as they hop between available adjacent sites. However, this process is counteracted by the elec...