A thermodynamic theory of electron correlation effects in narrow-band systems
Abstract
The problem of electron correlation effects in narrow bands at nonzero temperatures is analyzed in terms of a formalism introduced by Spalek et al. in which the correlated motion of the electrons is expressed through a band narrowing factor $\Phi$ which reflects the restricted motion of the electrons due to the on-site Coulomb interaction, U, between them. The thermodynamic properties of the correlated electron system at nonzero temperatures are discussed in terms of two different models: (a) a two-phase model in which the correlated system is composed of itinerant and localized particles, each with an appropriate weight which is calculated self-consistently and (b) a one-phase model in which the correlated electron system is represented solely in terms of a narrow band Fermi fluid. Our results indicate that both approaches lead to phase diagrams exhibiting qualitatively similar results. The treatment given predicts the occurrence, under appropriate conditions, of one or more discontinuous metal-insulator transitions with rising temperature at fixed values of U/W, which reproduce the principal qualitative features of experimental observations in systems such as (V$\sb{\rm 1-x}$Cr$\sb{\rm x})\sb2$O$\sb3$. For sufficiently strong correlation, the system remains in the insulating state throughout. The above results were obtained for a half-filled band and a rectangular density-of-states (DOS) function. For a less than half-filled band, the conditions under which the correlated metallic system with local moments transforms into a Fermi fluid with large effective mass are formulated. The effect of using a more realistic DOS function instead of the rectangular DOS considered earlier is investigated. The DOS function is seen to have a significant influence on the quantitative aspects of the theory although the results remain qualitatively similar. A formalism is introduced for incorporating the effects of antiferromagnetic ordering at T = 0. Preliminary results indicate that inclusion of antiferromagnetic ordering effects leads to a transition to the Mott-Hubbard insulating state for a (U/W) value lower than the (U/W)$\sb{\rm c}$ for the paramagnetic case.
Degree
Ph.D.
Advisors
Honig, Purdue University.
Subject Area
Chemistry
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