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In this work we use functional integral techniques to examine the nearest neighbour attractive Hubbard model on a quasi-2D lattice. It is a simple phenomenological model for the high-Tc cuprates that allows both extended (non-local) s-and d-wave singlet superconductivity as well as mixed symmetry states. The Hartree-Gor'kov mean field theory of the model has a finite temperature phase diagram which shows a transition from pure s-wave to pure d-wave superconductivity, via a mixed symmetry s + id state, as a function of doping. Including Gaussian fluctuations we examine the crossover from weak-coupling BCS superconductivity to the strong-coupling Bose-Einstein condensation of composite s-or d-wave bosons and comment on the origin and symmetry of the pseudogap.

A detailed Linear Combination of Atomic Orbitals (LCAO) tight-binding model is developed for the layered High-Temperature Superconductor (HTSC) cuprates. The band structure of these materials is described using a σ-band Hamiltonian employing Cu4s, Cu3d x 2 −y 2 , O2px and O2py atomic orbitals. The Fermi level and the shape of the resulting Fermi surface are fitted to recent Angle Resolved Photon Emission Spectroscopy (ARPES) data to realistically determine the dispersion in the conduction band. Electron-electron interactions and, ultimately, Cooper pairing is obtained by introducing a Heitler-London, two-electron exchange between adjacent orbitals within the CuO 2 plane. Finally, using the LCAO wavefunctions determined by the band structure fit, the Bardeen-Cooper-Schrieffer (BCS) type kernel is derived for interatomic exchange.

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