The effect of external magnetic field h on a static conductivity of Mott-Hubbard material which is described by the model with correlated hopping of electrons has been investigated. By means of canonical transformation, the effective Hamiltonian is obtained which takes into account strong intra-site Coulomb repulsion and correlated hopping. Using a variant of generalized Hartree-Fock approximation the single-electron Green function and quasiparticle energy spectrum of the model have been calculated. The static conductivity σ has been calculated as a function of h, electron concentration n and temperature T. The correlated hopping is shown to cause the electron-hole asymmetry of transport properties of narrow band materials

In the present paper we investigate a doubly orbitally degenerate narrowband model with correlated hopping. The model peculiarity takes 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 meanfield 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. Using the obtained energy spectrum we find criteria of metal-insulator transition. : 71.28.+d, 71.27.+a, 71.10.Fd, 71.30.+h Both theoretical analysis [1-3] and available experimental data [4] point out that the Hubbard model [5] should be generalized by taking into account orbital degeneration and correlated hopping. In the present paper we study a metal-insulator transition in the recently proposed [6] doubly orbitally degenerate narrow-band model with correlated hopping. The peculiarity of the model is the electron-hole asymmetry and the dependence of hopping integral on the average number of electrons per site, thus the model shows much better properties than, for example, the Hubbard model with doubly orbital degeneration. The model Hamiltonian is Key words: narrow energy bands, orbital degeneracy, metal-insulator transition, correlated hopping PACS