Superconductive states in the two-dimensional repulsive Hubbard model

Abstract

The investigation of the two-dimensional repulsive Hubbard model is continued for the case in which the Fermi level is close to one of the saddle Van Hove points of the quasiparticle energy function. The Bethe-Salpeter equation for the two-particle scattering amplitude and the system of Dyson-Gor'kov equations for normal and anomalous Green functions are considered. The closeness of the Van Hove point to the Fermi level makes the investigation substantially simpler. A new method of evaluating the kernel of the equations, i.e., the oneloop polarization diagram, is suggested. It is shown that a nontrivial Cooper pairing (the superposition of the pairings with odd angular momenta) appears in the model if and only if the Fermi level is close to one of the Van Hove points. The temperature of the superconductive phase transition is maximal for some special mutual location of the Fermi level and the Van Hove point. Two different superconductive solutions (modes) are found which are antisymmetric functions in the momentum representation. These modes coexist in close vicinity of the doping parameter value corresponding to the intersection of the Van Hove point and the Fermi level. The values of the energy gap for these modes are, generally speaking, different (the two different gap values are observed in some experiments). Bibliography: 18 titles.