Molecular viewpoint on high-temperature superconductivity Importance of orbital degeneracy

Abstract

It is shown that the antisymmetrized geminal power wavefunction (AGP) in the macroscopic limit and the Bardeen-Cooper-Schrieffer (BCS) supercon-ductivity 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, ∈ i 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 ∈ i =∈F at the Fermi level ∈F. The macroscopic contribution to the maximal pair occupation number which is responsible for the superconductivity is expressed as a mean value of Δi 2/[(∈ i −∈F)2+Δi 2]. The formulated non-zero temperature version of the eq...