Superconductivity in two-band systems with a small concentration of carriers

Superconductors with two characteristic features of high-temperature superconducting materials, i.e., a small concentration of charge carriers and overlapping energy bands on the Fermi surface, are considered. At T = 0, the order parameters Delta(n) and the chemical potential mu for the Bose condensate of local pairs (mu < 0) is determined in the mean field approximation. The equation for the bound state energy epsilon(b) is obtained and the relationship epsilon(b) = 2 mu is established. An application of the path integral method to the two-band model is developed and on this basis, the transition from the Fermi to the Bose pattern of elementary excitations in the presence of a two-particle bound state in the system is demonstrated. The expression for the temperature of Bose condensation T-k is obtained and the contribution of the residual boson interactions is estimated for systems with different dimensions.