The isotopic effect in highly correlated superconductors in the Anderson-Hubbard two-orbital model (in Russian)

Abstract

The two-orbital Hubbard model is used to obtain formula for the fermion excitation spectrum in the energy bands hybridized by Anderson’s interaction. A transition to the Hubbard operators diagonalizes the one-site part of the Hamiltonian and allows us to use Green’s function technique to take into account the interstitial hopping term, while studying the superconducting properties of the model. By proposing the dependence of the matrix element responsible for hybridization of p- and d- electronic states on the ampltitude of local vibrations of ions, we determined a value of isotopic effect a = ( M / T_c ) ( dT_c / dM ) (M – mass of ions). The dependence of a upon carrier density and energy parameters determining the intra-atomic correlation is analyzed. It was concluded, that at some values of parameters the isotopic effect in T_c can be large enough and the model under consideration can be used for the description of the isotopic shift in T_c for a number of superconductors.