Antiferromagnetism and high-temperature superconductivity

A model is presented describing superconductivity in close association with antiferromagnetism in a narrow-band system with electron correlations. We employ the Hubbard-Peierls Hamiltonian for weak to intermediate ratios between the on-site Coulomb repulsion and the electronic band width. Depending on the band structure and the electron number density antiferromagnetism arises, which for a nearly half-filled band gives rise to a Mott-Hubbard gap and resultant band splitting. The related density of energy states exhibits a singularity at the upper and lower edge of the lower and upper of the two split bands, respectively, if the lattice possesses the property of perfect nesting. The electron-phonon interaction is recast, by help of the method of canonical transformations, into a new form implying an attractive interaction between the quasiparticles in a Debye shell near the Fermi surface of each subband. A large effective interaction constant can be achieved and a BCS-type model for superconduction applies to each of the split bands if they are partially filled. Pairing arises between quasiparticles with parallel effective spin, i.e. in triplet states. The resulting gap equation is discussed in detail and the thermodynamic potential of the superconducting antiferromagnet is derived.