Hole superconductivity and the high-${\mathit{T}}_{\mathit{c}}$ oxides

We discuss predictions of the hole-pairing mechanism of superconductivity for various experimentally measurable properties of the high-${\mathit{T}}_{\mathit{c}}$ oxides. The model considered describes conduction by holes through the oxygen anion network in the high-${\mathit{T}}_{\mathit{c}}$ oxides, and pairing originates in a term in the Hamiltonian describing an enhanced hopping amplitude for a hole in the presence of other holes. The model includes on-site and nearest-neighbor Coulomb repulsions and different hopping amplitudes within and between planes. We use information from experiments to determine suitable ranges of parameters in the model and examine various properties of the superconducting state within this model using BCS theory. Among the most notable predictions of the model for the high-${\mathit{T}}_{\mathit{c}}$ oxides are: (1) the superconducting state is nearly isotropic despite the anisotropic band structure; (2) the pressure dependence of ${\mathit{T}}_{\mathit{c}}$ is very different for pressure applied perpendicular and parallel to the planes; and (3) the upper critical field and effective mass decrease rapidly and monotonically with hole doping, as a crossover occurs between strong- and weak-coupling regimes.