Electron correlations in narrow energy bands: modified polar model approach

Didukh Didukh,Kramar Kramar,Skorenkyy Skorenkyy

doi:10.5488/cmp.11.3.443

Abstract

The electron correlations in narrow energy bands are examined within the framework of the modied form of polar model. This model permits to analyze the effect of strong Coulomb correlation, inter-atomic exchange and correlated hopping of electrons and explain some peculiarities of the properties of narrow-band materials, namely the metal-insulator transition with an increase of temperature, nonlinear concentration dependence of Curie temperature and peculiarities of transport properties of electronic subsystem. Using a variant of generalized Hartree-Fock approximation, the single-electron Green’s function and quasi-particle energy spectrum of the model are calculated. Metal-insulator transition with the change of temperature is investigated in a system with correlated hopping. Processes of ferromagnetic ordering stabilization in the system with various forms of electronic DOS are studied. The static conductivity and effective spin-dependent masses of current carriers are calculated as a function of electron concentration at various DOS forms. The correlated hopping is shown to cause the electron-hole asymmetry of transport and ferromagnetic properties of narrow band materials.

Highlights

Polar model of crystal, developed on the basis of pioneering work of Schubin and Wonsowsky [1], proved to have rich physical content
We argue that the form of non-interacting density of states (DOS) substantially effects the critical electron concentration n1 at which ferromagnetic ordering occurs as well as electron concentration n2 at which magnetic moment becomes saturated
In the case of DOS with a peak near the band-edge (a = 0), the region of ferromagnetic ordering is shifted to low electron concentration values and the difference ∆E0FM/w increases, which leads to a substantial increase of Curie temperature

Summary

Introduction

Polar model of crystal, developed on the basis of pioneering work of Schubin and Wonsowsky [1], proved to have rich physical content. The disadvantages mentioned above were partially removed in a “new form of polar model” of Glauberman, Vladimirov and Stasyuk [4,5,6], where a rigorous algorithm of the transition from electron operators to the so-called “site elementary excitation” operators was elaborated. For the latter, exact commutation relations of two types, namely quasifermi and quasibose, were established. Transition operators Xikl (Hubbard operators) were introduced and in papers [8,9] the relation between electron and configuration representations: ais = Xi0s − ηsXis2,.

Modified form of polar model

Metal-insulator transition at increase of temperature

Ferromagnetic ordering in the model

Peculiarities of the electronic conductivity

Conclusions