An Effective Interaction Approach to Anisotropic Superconductors Beyond the Weak Coupling Theory—An Origin of the d-wave Symmetry in High-T c Cuprate

Abstract

We propose an effective interaction approach to superconducting systems which is adapted to periodic systems and intermediate net coupling between charge carriers by phonon mediated and Coulomb repulsive interactions. A coupling function of effective interaction is given for homogeneous field beyond the weak coupling approximation by using a generalized intermediate coupling method. Adequate kernel for the periodic systems is also reduced to that coupling function in homogeneous field and the Fourier coefficients relevant to the Bloch function. Within the present approach we discuss the symmetry of the superconducting gap in cuprate under the assumption that a nonbonding band filled by 2p_σ electrons exists in an undoped system and that doped holes occupy orbitals in this band. Those orbitals are represented by linear combinations of p x and p y functions. It is argued, in the tetragonal limit, that the symmetry of the gap function is d-wave-like on account of the products of orbital functions in combination of singlet spin-pair in the kernel.