Molecular viewpoint on high-temperature superconductivity importance of orbital degeneracy

It is shown that the antisymmetrized geminal power wavefunction (AGP) in the macroscopic limit and the Bardeen-Cooper-Schrieffer (BCS) superconductivity model with fixed mean number of electrons coincide to arbitrary order in deviations from the extreme-type function which is considered as the carrier of the superconductivity property. Variational equations for the AGP in the macroscopic limit are formulated in terms of two sets of parameters, εi and Δi, which under simplifying assumptions reduce to eigenvalues of the open-shell Roothaan one-electron Hamiltonian and to the BCS energy gap parameter, respectively. The superconducting state is shown to be stable for the solution of these equations with a macroscopic number of non-zero Δi and of degenerate εi=εF at the Fermi level εF.