Superconductivity in a two-band system with low carrier density
The review of works about the study of the thermodynamic properties of the superconductors with energy bands overlapping on Fermi surface is done. The base of the review is Moscalenco's model1 with the formation of cooper pairs of electrons inside each energy band and their transition as a whole entity from one band to another. The model was generalized in order to consider the interband pairings of electrons in addition to the pairings that have been taken into account in Ref. 1. The main system of equations in this theory of superconductivity is derived for the two-band systems at arbitrary density of charge carriers (including the very low densities). The detailed studies of dependences of the temperature of superconducting transition TC, the jump of heat capacity (CS-CN), as well as the chemical potential μ on the density of charge carriers are made. Singularities in the behavior of the two-band superconductors at low densities of charge carriers (μ~TC) are revealed. There has been studies on the influence of the additional pairings of electrons that result in the formation of the cooper pairs of electrons from different energy bands on the thermodynamic properties of the system. Both phonon and non-phonon mechanisms of superconductivity in the BCS scenario of the formation of superconducting pairs (μ>0) have been taken into account. The theory of superconductivity in the mean-field approximation at T = 0 in the picture of Bose condensation of localized pairs (Schaffroth's scenario μ<0) is built. The technique of functional integration with regard to the two-band system is developed and the crossover from Fermi to Bose picture of elementary excitations at T≠0 with the two-particle bound state in the system has been shown. The temperature of Bose condensation TK is determined and the influence of the overlapping of energy bands on Fermi surface onto Bose condensation of localized pairs is studied.