Group theoretical identification of active localized orbital space in high T_c cuprate superconductors

There is a widely shared consensus that the pair condensate wavefunction in cuprate superconductors has a dominant d_{x2 - y2} symmetry. In this paper a group theoretical analysis of the pair condensate wavefunction in real space for cuprate superconductors is presented. The analysis indicates that there is a degenerate pair of active bands in cuprate superconductors which are principally derived from localized e-orbitals and two possible singlet pair states formed from two different orbitals with symmetries a₁, b₁ or a₂, b₂ and all three may contribute to the condensate wavefunction. Hund's rule and the experimental observation that singlet pairing with a short coherence length occurs in cuprate superconductors, indicates that the first option is the most likely candidate in these materials and that hole doping mainly occurs from ¹B₁ pairs of e-orbitals giving rise to singlet electron pairing and the phenomenon of high T_c cuprate superconductivity.