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, Є_i, and ∆i 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 ∆i and of degenerate Єi = Є_F at the Fermi level Є_F. The macroscopic contribution to the maximal pair occupation number which is responsible for the superconductivity is expressed as a mean value of ∆_i²/[(Є_i - Є_F)^[1] + ∆i2]. The formulated non-zero temperature version of the equations for Є_i, ∆i is able to describe the superconducting phase transition. On this ground the necessary condition of stabilization of the superconducting state is formulated that is the existence of the macroscopic-fold near-degenerate and almost half-filled level. As is shown it is realized in the energy band structure of doped fullerides, copper oxide ceramics and perovskite-type crystals, e.g. BaBi0₃. The additional requirement of negativity of exchange interelectron-interaction integrals may be satisfied not only by the known vibronic mechanism but also, as is demonstrated, by the polarization potential of an environment in a plane layer of stratum structures.