Spin fluctuations and high-temperature superconductivity in cuprates

To describe the cuprate superconductors, models of strongly correlated electronic systems, such as the Hubbard or t−J models, are commonly employed. To study these models, projected (Hubbard) operators have to be used. Due to the unconventional commutation relations for the Hubbard operators, a specific kinematical interaction of electrons with spin and charge fluctuations emerges. The interaction is induced by the intraband hopping with a coupling parameter of the order of the kinetic energy of electrons  W which is much larger than the antiferromagnetic exchange interaction J induced by the interband hopping. This review presents a consistent microscopic theory of spin excitations and superconductivity for cuprates where these interactions are taken into account within the Hubbard operator technique. The low-energy spin excitations are considered for the t-J model, while the electronic properties are studied using the two-subband extended Hubbard model where the intersite Coulomb repulsion V and electron-phonon interaction are taken into account.