Dynamical effects of the electron–electron interaction in binary alloys with off-diagonal disorder are described in a self-consistent theory obtained by unifying a local ladder approximation for the random Hubbard model and a modified CPA. Numerical results are presented for partially averaged densities of states, self-energies which fulfil the Luttinger theorem, and effective two-particle vertices. The totally averaged density of states exhibits tails with strongly damped correlation humps.

The transition temperature Tc of strong-coupling superconducting alloys AcB1-c is determined with emphasis to tight-binding. Local random Eliashberg-type equations are configuration averaged by means of an effective mass operator on the basis of the CPA. Contrary to the McMillan form the resulting Tc formula involves two different phonon-mediated coupling parameters. The electron-phonon mass enhancement is originated from a complex renormalization factor.

Localization effects on the superconducting transition temperature T c are examined in strongly disordered three-dimensional systems. A tight-binding formulation of strong-coupling superconductivity is combined, after configuration averaging, with the selfconsistent treatment of Anderson localization developed by Wollhardt and Wölfle. The Coulomb interaction becomes retarded via the joint local density of states, giving rise to an enhancement of the pseudopotential. Numerical T c results as a function of disorder are compared with another theoretical work and experimental values for some high- T c materials.

The conductivity in disordered systems is calculated in terms of electron localisation, at dimensionality d=3 and temperature T=0, within tight-binding models with rectangular, Gaussian, Lorentzian and semi-elliptic probability distributions for the site energies. The method is based on a localisation approach in the sense of Vollhardt and Wolfle (1980, 1982) combined with Velicky’s coherent potential approximation framework for the conductivity under the assumption of a semi-elliptic shape for the unperturbed band. Numerical results for DC conductivities, the critical disorder of the metal-insulator transition and mobility edge trajectories are presented with emphasis on the similarities with and differences from earlier work with and without a conductivity pattern. The sensitivity of the critical disorder to the upper momentum cut-off is tested quantitatively.

The Schrieffer-Wolff transformation of the large-negative-U Hubbard model is performed in detail. Similarities to and differences from the canonical transformation of the large-positive-U Hamiltonian into the t-J model are discussed.

Within the slave-boson approach to the t-J model of high-Tc superconductivity, the vertex of the spinon-mediated holon-holon interaction is exploited in detail to find out the critical temperature of holon pairing.

The indirect exchange interaction between localized Cu spins via mobile O holes is derived from the three-band Anderson lattice model for copper oxides for infinite Hubbard repulsion at Cu sites. By means of two nested canonical transformations, Ruderman-Kittel-Kasuya-Yosida (RKKY) and superexchange interactions are found in the fourth order of the Cu-O hybridization amplitude, where both O bands are consequently taken into account. For nearest neighbours the RKKY coupling and the superexchange integral , which increase with the direct O-O transfer, differ in sign and undergo a sign change upon doping. overcompensates .

A relativistic version of the Lawrence-Doniach model is formulated to break the local U(1) gauge symmetry in analogy to the Higgs mechanism. Thereby the global U(1) invariance is spontaneously broken via the superconducting condensate. The resulting differential-difference equations for the order parameter, the in-plane and interplane components of the vector potential are of the Klein-Gordon, Proca and sine-Gordon type, respectively. A comparison with the standard sine-Gordon equation for the superconducting phase difference is given in the London limit. The present dynamical scheme is applicable to high-Tc cuprates with one layer per unit cell and weak interlayer Josephson tunneling.

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