ELECTRON CORRELATIONS IN NARROW ENERGY BANDS: GROUND STATE ENERGY AND METAL-INSULATOR TRANSITION

Didukh Didukh,Skorenkyy Skorenkyy

doi:10.5488/cmp.3.4.787

Abstract

The electron correlations in narrow energy bands are examined within the framework of the Hubbard model. The single-particle Green function and energy spectrum are obtained in a paramagnetic state at half-filling by means of a new two-pole approximation. Analytical expressions for the energy gap, polar states concentration and energy of the system are found in the ground state. Metal-insulator transitions in the model at the change of bandwidth or temperature are investigated. The results obtained are used for interpretation of some experimental data in narrow-band materials.

Highlights

Among the metal-insulator transitions (MIT) observed in narrow-band materials of great interest are the transitions from paramagnetic metal state to paramagnetic insulator state at the increase of temperature exhibited by the systems NiS2−xSex [1,2,3], (V1−xCrx)2O3 [1,4] and Y1−xCaxTiO3 [5,6]; in these systems the paramagnetic insulator – paramagnetic metal transitions under external pressure are observed as well
The two-pole approaches in the Hubbard model and the Hubbard bands conception have been useful in understanding the peculiarities of electric and magnetic properties of narrow-band materials [1,10]
U 2 + t2(k) instead of U 2 + 4d2t2(k). This leads to the series of distinctions between the results of this work and the results of work [13] (d(U/w)–dependence, the condition of metal-insulator transition, etc); at the same time expression (2.21) depends on polar state concentration similar to the respective expression in work [13]

Summary

Introduction

Among the metal-insulator transitions (MIT) observed in narrow-band materials of great interest are the transitions from paramagnetic metal state to paramagnetic insulator state at the increase of temperature exhibited by the systems NiS2−xSex [1,2,3], (V1−xCrx)2O3 [1,4] and Y1−xCaxTiO3 [5,6]; in these systems the paramagnetic insulator – paramagnetic metal transitions under external pressure are observed as well. Hubbard model is the simplest model describing MIT in the materials with narrow energy bands. This model describes a single non-degenerate band of electrons with the local Coulomb interaction. L.Didukh, Yu.Skorenkyy intraatomic Coulomb repulsion of two electrons of the opposite spins This model is used intensively (for recent reviews see [1,8,9,10]) in order to describe the peculiarities of physical properties of narrow-band materials; in this connection two-pole approaches seem to be attractive. The two-pole approaches in the Hubbard model and the Hubbard bands conception (being caused by the two-pole approximation) have been useful in understanding the peculiarities of electric and magnetic properties of narrow-band materials [1,10]. The observable transitions from an insulating state to a metallic state at the increase of a bandwidth, and from a metallic state to an insulating state at the increasing temperature are explained

Single-particle Green function and energy spectrum

Energy gap and polar states concentration

Ground state energy

Conclusions