Symmetry of the superconducting gap function from electron scattering by interacting tunneling units

The symmetry of the gap function is derived for a system in which the conduction electrons are scattered by elastically interacting tunneling units, causing pairing and superconductivity. For specific examples of tunneling units found in experiments on a number of high T c materials we obtain; (i) a strongly anisotropic effective electron-electron interaction due to the anisotropic coupling to the tunneling units; (ii) a strongly anisotropic gap in k-space even for a spherical fermi surface; (iii) a high transition temperature; (iv) a gap function with nodes and a combination of s and d x 2− y 2 symmetry.