Theory of Superconductivity in Strongly Correlated Materials: Application to Cuprate Superconductors

A microscopic theory of superconductivity in systems with strong electron correlations is considered within the Hubbard model. The Dyson equation for the matrix Green function in terms of the Hubbard operators is derived and solved in the noncrossing approximation for the self-energy. Two channels of superconducting pairing are revealed: mediated by antiferromagnetic (AFM) exchange and spin-fluctuations. It is proved that AFM exchange interaction results in pairing of all electrons in the conduction band and high T-c proportional to the Fermi energy. T-c dependence on lattice constants (or pressure) and an oxygen isotope shift of T-c are explained.