The possibility of forming coupled pairs in the periodic Anderson model

We investigate the generalized periodic Anderson model describing two group s of strongly correlated (d- and f-) electrons with local hybridization of states and d-electron hopping between lattice sites from the standpoint of the possible appearance of coupled electron pairs in it. The atomic limit o f this model admits an exact solution based on the canonical transformation method. The renormalized energy spectrum of the local model is divided int o low- and high-energy parts separated by an interval of the order of the C oulomb electron-repulsion energy. The projection of the Hamiltonian on the states in the low-energy part of the spectrum leads to pair-interaction ter ms appearing for electrons belonging to d- and f-orbitals and to their poss ible tunneling between these orbitals. In this case, the terms in the Hamil tonian that are due to ion energies and electron hopping are strongly corre lated and can be realized only between states that are not twice occupied. The resulting Hamiltonian no longer involves strong couplings, which are su ppressed by quantum fluctuations of state hybridization. After linearizing this Hamiltonian in the mean-field approximation, we find the quasiparticle energy spectrum and outline a method for attaining self-consistency of the order parameters of the superconducting phase. For simplicity, we perform all calculations for a symmetric Anderson model in which the energies of tw ice occupied d- and f-orbitals are assumed to be the same.