Electron correlations in narrow energy bands: modified polar model approach

Abstract

The electron correlations in narrow energy bands are examined within the framework of the modified 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.

Electron-hole asymmetry in electron systems with orbital degeneracy and correlated hopping

“…On the contrary, the application of the external pressure or doping in systems (V 1−𝑥 Cr 𝑥 ) 2 O 3 and NiS 2−𝑥 Se 𝑥 leads to metalization [1] by increasing the energy subbands width and reducing Δ 𝑤 below the critical value. The critical values for the partial case when there is no correlated hopping are in agreement with the results of paper [38] for non-degenerated Hubbard model and paper [46] for a triply degenerated model.…”

“…In terminology of papers [26,53], we study here only the low-energy sector of the model to compare the effects produced by the degeneracy of the energy levels and the correlated hopping, both removing the particle-hole symmetry. Concentrations of doublons appear to be an important parameter in this approach that allows one to naturally introduce a dependence of the energy spectrum The non-operator coefficients ε b (k),ε b (k), ε h (k),ε h (k) can be obtained by a procedure described in detail in paper [38] in the paramagnetic case at n = 1 for the doubly degenerated model as…”

“…In section 3 the concentrations of empty sites (holes) and doubly occupied sites close to metal-insulator transition at the electron concentration n = 1 for models with non-degenerated, doubly-and triply-degenerated energy levels are calculated. For calculation of quasiparticle energy spectra, the nonperturbative approach, generalized mean-field approximation [37,38] is used. Section 4 presents our conclusions on the role of correlated hopping in models with orbital degeneracy.…”

“…We make use of the completeness condition for the 𝑋-operator set to obtain constraints 𝑐 + 2𝑠 + 𝑑 = 1 for a non-degenerate model, 𝑐 + 4𝑠 + 6𝑑 = 1 for a model with double degeneracy, 𝑐 + 6𝑠 + 6𝑑 = 1 for a model with triple degeneracy at strong Coulomb correlation and at strong Hund's coupling. The non-operator coefficients 𝜀 𝑏 (k), ε𝑏 (k), 𝜀 ℎ (k), εℎ (k) can be obtained by a procedure described in detail in paper [38] in the paramagnetic case at 𝑛 = 1 for the doubly degenerated model as…”

“…For the generalized Hubbard model with correlated hopping [38], the doublon concentration is given by…”