A model for description of materials with narrow energy bands is proposed. It is shown that in narrow-band materials electron-hole symmetry is absent in contrast to the Hubbard model. In this paper metal-insulator transition is studied. The obtained results are compared with experimental data for narrow-band materials. Some specific narrow-band effects are discussed.

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In the present paper we propose a doubly orbitally degenerate narrow-band model with correlated hopping. The peculiarity of the model is taking into account the matrix element of electron-electron interaction which describes intersite hoppings of electrons. In particular, this leads to the concentration dependence of the effective hopping integral. The cases of the strong and weak Hund's coupling are considered. By means of a generalized mean-field approximation the single-particle Green function and quasiparticle energy spectrum are calculated. Metal-insulator transition is studied in the model at different integer values of the electron concentration. With the help of the obtained energy spectrum we find energy gap width and criteria of metal-insulator transition.

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In the present paper metal-insulator transition is studied in a generalized Hubbard model with correlated hopping at half-filling and zero temperature. Single-particle Green function and energy spectrum of electron system are calculated. The expressions for energy gap width and the concentration of polar states (holes or doublons) are obtained. The conditions for metallic and insulating states are found.